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REVIEW 4 major objections 6 minor 109 references

Synthetic Data for Portfolios: A Throw of the Dice Will Never Abolish Chance

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper proves that generating unbounded synthetic returns concentrates estimates on the model's learned bias, and that generic generative models learn the high-variance principal components that portfolio construction needs least.

desk verdict Honest and worth engaging: the sample-size warning is clean, the evaluation work is strong, but the portfolio-paradox claim leans on a linear-Gaussian theorem that does not obviously cover real GANs. read the letter →

arxiv 2501.03993 v6 pith:6WQORUMD submitted 2025-01-07 q-fin.PM q-fin.RMstat.ML

Adil Rengim Cetingoz , Charles-Albert Lehalle This is my paper · ORCID
classification q-fin.PMq-fin.RMstat.ML MSC 91G1062G20
keywords generativemodelssyntheticdatamachinelearningadversarialnetworkshigh-dimensionalreturnsprincipalcomponentanalysisportfolioconstructionidentifiability
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that synthetic data cannot outrun the finite sample it was trained on, and that generic generative models are structurally misaligned with portfolio construction. For statistics such as means, variances, and covariances (the $U$-statistic class), if the model's learned value is biased by at least the tolerance $b$, then generating ever more data makes the estimate converge to the bias: $\lim_{\tilde n\to\infty} P(|U_{\tilde n}-\theta|\le b)=0$. The paper also claims that mean-variance and long-short portfolios depend disproportionately on low-variance principal components, while standard distribution-matching generators learn high-variance components best, so a generic GAN will be most accurate exactly where the portfolio cares least. To escape this, it builds a market generator that separates a few GAN-modeled factors from heavy-tailed $t$-distributed residuals and shows the resulting 433-asset simulations match conventional statistical checks; it then proposes a mean-reversion Sharpe-ratio profile and a regurgitative identifiability test as application-aware evaluations.

What carries the argument

The argument runs on three mechanisms. The finite-sample result uses $U$-statistics and Berry-Esseen-type error bounds: Proposition 1 bounds the probability that a synthetic-sample statistic lands within tolerance of the truth, and Corollary 2 takes the $\tilde n\to\infty$ limit to show that excess generation concentrates on the learning bias. The portfolio paradox uses a principal-space rewrite of mean-variance optimization: Proposition 4 shows the inverse covariance matrix rescales each eigen-direction by $1/\lambda_i$, and Corollary 7 shows the same eigenvector perturbation costs far more on a low-variance factor. The constructive half is the market generator itself: standardized returns are split by a random-matrix threshold into a few principal factor series, the factor series are clustered and modeled by temporal-convolutional GANs, and the residuals are modeled by mixtures of $t$ distributions; Equation (16) reassembles these pieces into simulated return paths.

What would settle it

Train a generic GAN on multivariate Gaussian data whose covariance has eigenvalues spanning several orders of magnitude, generate a very long sample, and compare the estimated covariance's eigenvectors and eigenvalues to the truth component by component; if the low-variance directions are not learned substantially worse than the high-variance ones, the claimed mismatch between generic generators and portfolio construction is falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that initial sample size is an irreducible constraint: for any $U$-statistic, if the generative model's learned statistic $\tilde\theta_n$ differs from the true $\theta$ by at least the tolerance $b$, then Corollary 2 gives $\lim_{\tilde n\to\infty} P(|U_{\tilde n}-\theta|\le b)=0$, so the synthetic estimate concentrates on the model's bias. It then derives a structural paradox: mean-variance portfolio weights multiply expected returns by the inverse covariance matrix, so low-variance principal components matter most, while distribution-matching generators are shown (in the linear-Gaussian population case, and argued for general GANs) to reproduce the highest-variance components first; Proposition 6 and Corollary 7 quantify that the same eigenvector error moves a portfolio far more on a low-variance factor. As a constructive answer, the paper builds a market generator that separates a few principal factors from residual returns, models the factors with clustered temporal-convolutional GANs and the residuals with mixtures of $t$ distributions, and validates the simulated 433-asset universe against in-sample and out-of-sample data.

Load-bearing premise

The load-bearing premise is that what holds for linear generators on Gaussian data—learning the highest-variance components best—carries over to realistic nonlinear GANs, which is what makes off-the-shelf generative models mismatched with long-short portfolios.

Editorial extensions

If this is right

  • A practitioner estimating a statistic should keep the synthetic sample size of the same order as the training sample; generating orders of magnitude more data only tightens confidence intervals around the model's bias.
  • Generative models for portfolio work should be evaluated component-wise in principal space, measuring error on low-variance directions rather than only on marginal distributions or overall distance.
  • Long-short backtests built with generic GANs should be treated with suspicion unless the generator explicitly models low-variance factors; block bootstrap is a natural baseline because its confidence intervals stay anchored to history.
  • The proposed factor-based market generator passes conventional in-sample checks (marginals, tails, correlations, dynamic correlation, volatility clustering) on 433 US daily return series, which the paper presents as evidence that the pitfalls can be turned around.
  • Using the Sharpe-ratio profile of a mean-reversion strategy across look-back windows, the paper shows the regurgitative retraining test can flag that its own model class should not be trusted for time scales longer than about one month.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The bias-concentration result implies a 'synthetic data budget' for any downstream estimator, and by the paper's own extension to L-statistics it should apply to Value-at-Risk and Expected Shortfall: more generated scenarios beyond the budget narrows the estimate around the model's bias.
  • The same principal-space reasoning suggests a cheap diagnostic for any financial generator: compute per-component accuracy of the generated covariance and reject models whose error grows as eigenvalues shrink, even if their marginal and portfolio-level statistics look right.
  • A testable extension is to run the mean-reversion Sharpe-profile and regurgitative identifiability test on other generator families (diffusion models, variational autoencoders, bootstraps) to see whether identifiability rankings predict out-of-sample backtest quality.
  • The regurgitative test itself generalizes: any simulator class that cannot recover its own ground-truth risk-reward profile after one generation-retraining cycle is likely to mislead on real data, making identifiability a model-selection criterion rather than just a diagnostic.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper studies limitations of generative models for financial portfolio construction. Section 2.1 derives, under Assumption 1, a Berry-Esseen-type bound for U-statistics computed on synthetic data and shows that if the learned statistic is biased by at least the tolerance (|a_n| >= b), the probability of approximating the true statistic tends to zero as the synthetic sample size grows. Section 2.2 argues that Markowitz-type portfolios scale down high-variance principal components via the inverse covariance matrix, and combines this with a linear-Gaussian result of Feizi et al. to claim that generic generative models learn high-variance components best and are therefore mismatched with long-short portfolios. Sections 3 and 4 propose a market generator (PCA factor decomposition, clustered TCN-based GANs for scaled factors, Student-t residuals) and evaluate it on 433 S&P500 stocks, reporting marginal, tail, correlation, and portfolio-level metrics. Section 5 tests the generator on Sharpe-ratio profiles of mean-reversion strategies against block bootstrap and proposes a 'regurgitative training' identifiability test. The paper concludes that initial sample size is crucial, that generic models are poorly suited to portfolio construction, and that the proposed pipeline plus the proposed evaluation protocol addresses these issues.

Significance. Conditional on its assumptions, the paper contains several genuinely useful elements. The Berry-Esseen argument (Proposition 1, Corollary 2) is a clean formalization of the 'more synthetic data does not fix bias' intuition, and the algebraic observation in Proposition 4 and Corollary 7 that portfolio construction amplifies low-variance principal components is correct and clearly presented. The proposed pipeline is carefully described, with architecture and training details in Appendix C, and the empirical evaluation is unusually thorough: out-of-sample checks, confidence intervals, stylized-fact validation, and a comparison with block bootstrap. The proposal to use the Sharpe-ratio profile of mean-reversion strategies across time scales as a benchmark is valuable and falsifiable. The main weakness is that the portfolio paradox rests on an extrapolation from a linear-Gaussian W2 theorem to general nonlinear generators, and the paper's own empirical section does not yet close that gap; the identifiability test also needs an operational decision rule.

major comments (4)
  1. [Section 2.2, Theorem 5] The central negative claim of the paper—that generic generative models are mismatched with long-short portfolio construction—rests on Theorem 5, quoted from Feizi et al. (2017), which is proven only for linear generators, Gaussian data, the p=2 Wasserstein distance, and the population limit. The manuscript's bridge is the sentence 'Although simplified, the task described in Theorem 5 is quite similar to what most generative models aim to achieve' (Section 2.2). This is an assertion, not a derivation; the paper's own generator is a nonlinear TCN trained with the Jensen-Shannon objective (Section 3.2.2), which is outside the theorem's scope. Proposition 4 and Corollary 7 establish the portfolio side, but without a result, or direct empirical measurement, on how per-eigenvector errors of nonlinear generators depend on the spectrum, the paradox is not established. Please either prove an extension for nonlinear generators (or for the loss actually used), add an empirical analysis measuring per-eigenvector errors for several architectures and losses, or explicitly reframe the paradox as a conjecture and moderate the conclusions in Sections 1 and 6 accordingly.
  2. [Section 2.1, Assumption 1 and Corollary 2] Corollary 2 is valid as a conditional statement, but Assumption 1 is not a theorem and no empirical evidence is provided for it. The paper's own discussion (Section 2.1) states only that 'this assumption states that a statistic computed on synthetic data lies in between its true underlying value and its empirical value,' which is a different and stronger statement than the formal 'inversely related to a power of n.' More importantly, the corollary requires |a_n| >= b; for a well-trained model and a sufficiently loose tolerance b, |a_n| < b and additional synthetic data are harmless. The blanket conclusion 'generating more data points ... introduces a bias' (Section 2.1) is therefore not supported without an upper bound on |a_n| or an empirical check. Please prove a bound on a_n for a relevant model class, or state clearly throughout that Corollary 2 holds only under Assumption 1 and |a_n| >= b.
  3. [Section 5.1, Table 9] The empirical section does not currently demonstrate that the proposed pipeline 'turns around' the paradox for long-short portfolios. In Table 9, the long-short market-generator intervals are wide and frequently do not contain the in-sample or out-of-sample Sharpe ratio, e.g., h=1: median 0.38, 95% CI [-0.36, 1.05], while IS=0.08 and OoS=0.77; h=13: median 0.03, CI [-0.40, 0.56], IS=0.44, OoS=0.22. The block-bootstrap intervals are also wide, and no coverage or calibration statistic is reported. Please provide a quantitative comparison of the two methods, e.g., coverage of in-sample and out-of-sample curves by the confidence bands, average interval width, or a proper scoring rule, so that the claim that the market generator is preferable for long-short evaluation is testable.
  4. [Section 5.2, Figure 16 and Table 11] The proposed identifiability test lacks a decision rule. As described, the test trains a 'regurgitative' model on data generated by the reference model and then visually compares Sharpe-ratio profiles. A badly misspecified model that is nevertheless identifiable within its own class would pass this test, so the method cannot, on its own, 'detect poor models' (Section 5.2) in the sense of closeness to the true market. The conclusion that the class 'should probably not be used for time scales longer than one month' is based on eyeballing Figure 16 rather than on a stated statistical criterion. Please define an explicit pass/fail measure, such as coverage of the true curve at a nominal level or a distance threshold, and state what types of misspecification the test is and is not sensitive to.
minor comments (6)
  1. [Section 4.2.2, Table 8] The near-exact in-sample Sharpe ratio (1.09 vs 1.08) is partly by construction, since the generator injects sample means and volatilities, as the text notes; please state this caveat directly in the caption or in the paragraph introducing Table 8.
  2. [Section 3.1] Typo: 'That for, we will first review' should be 'To that end, we will first review'.
  3. [Figures 19, 20, and 21] The figure titles contain the misspelling 'Syntetic' and should read 'Synthetic'.
  4. [Section 3.2.4 heading] The heading 'V ariance correction with non-normal white noise' contains an unwanted space; it should be 'Variance correction with non-normal white noise'.
  5. [Section 2.1, L-statistics remark] The extension to L-statistics is mentioned without proof or a precise reference to the asymptotics needed for Value-at-Risk and Expected Shortfall; please add a short argument or a more specific citation.
  6. [Data Availability Statement] The reproducibility of the empirical study would be improved by releasing code or a detailed data-processing script, since the data are available only upon request.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the sample-size bias theorem is a direct CLT consequence, the portfolio paradox rests on an external theorem with an acknowledged extrapolation, and the built-in Sharpe reproduction and model-as-ground-truth test are explicitly flagged by the authors rather than presented as independent predictions.

full rationale

The paper's central derivation chain is not circular. Corollary 2 follows from the Berry-Esseen-type bound for U-statistics and the definition of a_n as the learning accuracy, so 'more synthetic data concentrates on the learned bias' is a mathematical consequence rather than a fitted prediction; no parameter is fit to make this true. The portfolio paradox combines Proposition 4/Corollary 7 (portfolio weights amplify low-variance eigenvectors) with Theorem 5, an external result from Feizi et al. 2017 for linear generators on Gaussian data. The paper's extension to generic GANs rests on an explicit sentence saying the task is 'quite similar' to what most generative models aim to achieve; this is an extrapolation and a correctness risk, but it is not circular because Theorem 5 is not the paper's own prior conclusion and is not defined in terms of the portfolio result. The near-exact in-sample Sharpe ratio (1.09 vs 1.08) is indeed forced by construction, since Equation (16) injects the sample means and volatilities, but the paper openly states this is 'natural since the market generator uses sample means and sample variances of individual assets estimated in-sample'; it is presented as an in-sample descriptive check, not as an out-of-sample prediction or as load-bearing evidence for the theoretical claims. Similarly, the identifiability/regurgitative test deliberately uses the trained model as a known ground truth and is explicitly labeled as less informative than the true generative process; this is a designed identifiability check, not a hidden circularity. The only self-citation, [Capponi and Lehalle, 2023], appears in the introduction as context for machine learning interest in finance and is not load-bearing. The paper is self-contained against external data and benchmarks for its main claims, and the acknowledged built-in features do not advance the central argument.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The central sample-size result depends on Assumption 1, an unproved scaling relation. The portfolio paradox depends on extrapolating a linear-Gaussian GAN theorem to general GANs. The pipeline adds hand-chosen hyperparameters (m, s, nc) and distributional assumptions for residuals. No new entities are introduced.

free parameters (5)
  • number of factors m = 16
    Number of factors m=16 selected as eigenvalues above the Marcenko-Pastur bound lambda+=1.90; an alternative fit gives 44 factors, and no sensitivity analysis is reported.
  • memory length s = 63 days
    Memory length s=63 days used for GAN windows and clustering scores; chosen by the authors without a formal selection procedure.
  • number of clusters nc = 3
    Number of GAN clusters nc=3 from agglomerative clustering; the cluster count appears hand-selected.
  • residual Student-t parameters = per asset via MLE
    Per-asset Student-t parameters (degrees of freedom, location, scale) estimated by maximum likelihood; the mixture is simplified to a single Student-t, omitting skewness.
  • GAN hyperparameters = Appendix C
    Architecture and training hyperparameters (Appendix C) are fixed by hand; no validation-based tuning is described.
assumptions (7)
  • ad hoc to paper Assumption 1: the learning accuracy a_n = theta_tilde_n - theta is inversely related to a power of the initial sample size n.
    Invoked in Section 2.1 before Proposition 1; it is not proven and is the basis for Corollary 2.
  • standard math The data X_1,...,X_n are i.i.d. with finite moments, and U-statistics are the target estimators.
    Standard U-statistic framework (Serfling, Hoeffding) used in Section 2.1.
  • domain assumption The market covariance matrix follows the eigen-clipped model Sigma = P Delta P^T + lambda_c Q Q^T.
    Model (4) in Section 2.2; standard PCA factor assumption, not derived.
  • ad hoc to paper A generic generative model trained with Wasserstein distance learns high-variance PCs better than low-variance PCs, by extrapolating Theorem 5 of Feizi et al. (linear Gaussian case) to general GANs.
    Section 2.2; load-bearing for the portfolio paradox, no proof for nonlinear generators.
  • domain assumption Asset returns follow X(t) = (beta F(t) + Z(t)) * sigma + mu with independent factor and residual processes.
    Equation (11) in Section 3.2; modeling assumption for the proposed pipeline.
  • domain assumption Residual returns are i.i.d. across time and assets and can be modeled by a Student-t distribution.
    Section 3.2.4 and Section 4.1; simplifies residuals, supported by empirical correlations near zero but not exact.
  • domain assumption The reference generative model's output can serve as ground truth for the regurgitative identifiability test.
    Section 5.2; this is an internal self-consistency check, not validation against the true market process.

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Cite this review

Pith. "Pith review of Synthetic Data for Portfolios: A Throw of the Dice Will Never Abolish Chance." pith.science (2026). https://pith.science/paper/6WQORUMD

@misc{pith2026250103993,
  author       = {Pith},
  title        = {Pith review of: Synthetic Data for Portfolios: A Throw of the Dice Will Never Abolish Chance},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6WQORUMD}},
  note         = {Machine review of arXiv:2501.03993}
}
read the original abstract

Simulation methods have always been instrumental in finance, and data-driven methods with minimal model specification, commonly referred to as generative models, have attracted increasing attention, especially after the success of deep learning in a broad range of fields. However, the adoption of these models in financial applications has not matched the growing interest, probably due to the unique complexities and challenges of financial markets. This paper contributes to a deeper understanding of the limitations of generative models, particularly in portfolio and risk management. To this end, we begin by presenting theoretical results on the importance of initial sample size, and point out the potential pitfalls of generating far more data than originally available. We then highlight the inseparable nature of model development and the desired uses by touching on a paradox: usual generative models inherently care less about what is important for constructing portfolios (in particular the long-short ones). Based on these findings, we propose a pipeline for the generation of multivariate returns that meets conventional evaluation standards on a large universe of US equities while being compliant with stylized facts observed in asset returns and turning around the pitfalls we previously identified. Moreover, we insist on the need for more accurate evaluation methods, and suggest, through an example of mean-reversion strategies, a method designed to identify poor models for a given application based on regurgitative training, i.e. retraining the model using the data it has itself generated, which is commonly referred to in statistics as identifiability.

Figures

Figures reproduced from arXiv: 2501.03993 by the authors.

Figure 1
Figure 1. Illustration of the mentioned variables in the context of estimating a statistic using a [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Training pipeline of the generative model. [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
Figure 3
Figure 3. (Left) Eigenvalue distribution for the selected universe (black). Marcenko-Pastur [PITH_FULL_IMAGE:figures/full_fig_p023_3.png] view at source ↗
Figures from the paper (15 more)
Figure 4
Figure 4. Figure 4: Median non-linear time dependence at the level of different components. Volatility [PITH_FULL_IMAGE:figures/full_fig_p024_4.png]
Figure 5
Figure 5. Figure 5: Distribution of cross-asset correlations obtained from the lower triangle of the correla [PITH_FULL_IMAGE:figures/full_fig_p025_5.png]
Figure 6
Figure 6. Figure 6: Distribution of the empirical skewness (left) and kurtosis (middle) of the 433 stocks [PITH_FULL_IMAGE:figures/full_fig_p026_6.png]
Figure 7
Figure 7. Figure 7: Wasserstein distances between simulated and historical samples based on different [PITH_FULL_IMAGE:figures/full_fig_p028_7.png]
Figure 8
Figure 8. Figure 8: Volatility clustering and leverage effect scores computed on historical and simulated [PITH_FULL_IMAGE:figures/full_fig_p029_8.png]
Figure 9
Figure 9. Figure 9: Expected Shortfall at the level 99% and kurtosis computed on historical and simulated [PITH_FULL_IMAGE:figures/full_fig_p030_9.png]
Figure 10
Figure 10. Figure 10: Evolution of average correlations (using a rolling window of one-year) between assets [PITH_FULL_IMAGE:figures/full_fig_p032_10.png]
Figure 11
Figure 11. Figure 11: Returns of the equal-weighted portfolio computed on different samples. [PITH_FULL_IMAGE:figures/full_fig_p032_11.png]
Figure 12
Figure 12. Figure 12: Inter-temporal properties of the equal-weighted portfolio computed on different sam [PITH_FULL_IMAGE:figures/full_fig_p033_12.png]
Figure 13
Figure 13. Figure 13: Boxplots of Sharpe ratios of the long-only mean-reversion strategy for different look [PITH_FULL_IMAGE:figures/full_fig_p035_13.png]
Figure 14
Figure 14. Figure 14: Boxplots of Sharpe ratios of the long-short mean-reversion strategy for different look [PITH_FULL_IMAGE:figures/full_fig_p036_14.png]
Figure 15
Figure 15. Figure 15: (Left) The Sharpe ratio profile across time scales, computed on 100 simulated samples [PITH_FULL_IMAGE:figures/full_fig_p037_15.png]
Figure 16
Figure 16. Figure 16: Boxplots of Sharpe ratios of the long-short mean-reversion strategy for different look [PITH_FULL_IMAGE:figures/full_fig_p039_16.png]
Figure 17
Figure 17. Figure 17: Sample correlation matrices for factor-based, residual and original returns. [PITH_FULL_IMAGE:figures/full_fig_p053_17.png]
Figure 18
Figure 18. Figure 18: Correlation matrices computed on historical and one simulated sample. [PITH_FULL_IMAGE:figures/full_fig_p053_18.png]

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Reference graph

Works this paper leans on

109 extracted references · 54 canonical work pages

  1. [1]

    Aaronson, J., Burton, R., Dehling, H., Gilat, D., Hill, T., and Weiss, B. (1996). Strong laws for l-and u-statistics. Transactions of the American Mathematical Society , 348(7):2845--2866

    1996

  2. [2]

    S., and Wah, T

    Aghabozorgi, S., Shirkhorshidi, A. S., and Wah, T. Y. (2015). Time-series clustering--a decade review. Information Systems , 53:16--38

    2015

  3. [3]

    N., Bates, S., Fannjiang, C., Jordan, M

    Angelopoulos, A. N., Bates, S., Fannjiang, C., Jordan, M. I., and Zrnic, T. (2023). Prediction-powered inference. Science , 382(6671):669--674

    2023

  4. [4]

    Arjovsky, M., Chintala, S., and Bottou, L. (2017). Wasserstein GAN . arXiv:1701.07875 [cs, stat]

    arXiv 2017

  5. [5]

    S., Moskowitz, T

    Asness, C. S., Moskowitz, T. J., and Pedersen, L. H. (2013). Value and momentum everywhere. The Journal of Finance , 68(3):929--985

    2013

  6. [6]

    Assefa, S. (2020). Generating Synthetic Data in Finance : Opportunities , Challenges and Pitfalls . SSRN Electronic Journal

    2020

  7. [7]

    and Lee, J.-H

    Avellaneda, M. and Lee, J.-H. (2010). Statistical arbitrage in the us equities market. Quantitative Finance , 10(7):761--782

    2010

  8. [8]

    Ben Arous, G., Mei, S., Montanari, A., and Nica, M. (2019). The landscape of the spiked tensor model. Communications on Pure and Applied Mathematics , 72(11):2282--2330

    2019

Show all 109 references
  1. [9]

    Bentkus, V., Jing, B.-Y., and Zhou, W. (2009). On normal approximations to u-statistics. Annals of Probability , 37(6):2174--2199

    2009

  2. [10]

    Berkowitz, J. (1999). A coherent framework for stress-testing. Available at SSRN 181931

    1999

  3. [11]

    Bishop, C. M. (1995). Training with noise is equivalent to tikhonov regularization. Neural computation , 7(1):108--116

    1995

  4. [12]

    Black, F. (1986). Noise. The Journal of Finance , 41(3):528--543

    1986

  5. [13]

    Borji, A. (2018). Pros and Cons of GAN Evaluation Measures . arXiv:1802.03446 [cs]

    2018 arXiv

  6. [14]

    Bouchaud, J.-P., Matacz, A., and Potters, M. (2001). Leverage effect in financial markets: The retarded volatility model. Physical Review Letters , 87(22):228701

    2001

  7. [15]

    Boyd, S., Johansson, K., Kahn, R., Schiele, P., and Schmelzer, T. (2024). Markowitz portfolio construction at seventy. arXiv preprint arXiv:2401.05080

    2024 arXiv

  8. [16]

    Boyle, P. P. (1977). Options: A Monte Carlo approach . Journal of Financial Economics , 4(3):323--338

    1977

  9. [17]

    and Glasserman, P

    Broadie, M. and Glasserman, P. (1996). Estimating security price derivatives using simulation. Management Science , 42(2):269--285

    1996

  10. [18]

    Brown, T. B. (2020). Language models are few-shot learners. arXiv preprint arXiv:2005.14165

    2020 arXiv

  11. [19]

    Bryzgalova, S., Pelger, M., and Zhu, J. (2019). Forest Through the Trees : Building Cross - Sections of Stock Returns . SSRN Electronic Journal

    2019

  12. [20]

    P., and Wood, B

    Buehler, H., Horvath, B., Lyons, T., Arribas, I. P., and Wood, B. (2020). A data-driven market simulator for small data environments. arXiv preprint arXiv:2006.14498

    2020 arXiv

  13. [21]

    and Lehalle, C.-A

    Capponi, A. and Lehalle, C.-A. (2023). Machine learning and data sciences for financial markets. Technical report, Cambridge University Press

    2023

  14. [22]

    Caprioli, S., Cagliero, E., and Crupi, R. (2023). Quantifying Credit Portfolio sensitivity to asset correlations with interpretable generative neural networks. arXiv:2309.08652 [cs, q-fin]

    2023 arXiv

  15. [23]

    Carlstein, E. (1986). The use of subseries values for estimating the variance of a general statistic from a stationary sequence. The Annals of Statistics , pages 1171--1179

    1986

  16. [24]

    Carriere, J. F. (1996). Valuation of the early-exercise price for options using simulations and nonparametric regression. Insurance: Mathematics and Economics , 19(1):19--30

    1996

  17. [25]

    Chen, L. H. and Shao, Q.-M. (2007). Normal approximation for nonlinear statistics using a concentration inequality approach. Bernoulli , 13(2):581--599

    2007

  18. [26]

    Chen, M., Xu, R., Xu, Y., and Zhang, R. (2025). Diffusion factor models: Generating high-dimensional returns with factor structure. arXiv preprint arXiv:2504.06566

    2025

  19. [27]

    Cont, R. (2000). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance

    2000

  20. [28]

    Cont, R. (2010). Stylized properties of asset returns. Encyclopedia of Quantitative Finance

    2010

  21. [29]

    Cont, R., Cucuringu, M., Kochems, J., and Prenzel, F. (2023). Limit order book simulation with generative adversarial networks. Available at SSRN 4512356

    2023

  22. [30]

    Cont, R., Cucuringu, M., Xu, R., and Zhang, C. (2022). Tail- GAN : Nonparametric Scenario Generation for Tail Risk Estimation . arXiv:2203.01664 [q-fin]

    2022 arXiv

  23. [31]

    Cont, R., Potters, M., and Bouchaud, J.-P. (1997). Scaling in stock market data: stable laws and beyond. In Scale Invariance and Beyond: Les Houches Workshop, March 10--14, 1997 , pages 75--85. Springer

    1997

  24. [32]

    and Shi, S

    Da Silva, B. and Shi, S. S. (2019). Style transfer with time series: Generating synthetic financial data. arXiv preprint arXiv:1906.03232

    2019 arXiv

  25. [33]

    de Meer Pardo, F. (2019). Enriching financial datasets with generative adversarial networks. MS thesis, Delft University of Technology, The Netherlands

    2019

  26. [34]

    de Prado, M. M. L. (2020). Machine Learning for Asset Managers . Cambridge University Press

    2020

  27. [35]

    P., Laird, N

    Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of the royal statistical society: series B (methodological) , 39(1):1--22

    1977

  28. [36]

    Deng, J., Dong, W., Socher, R., Li, L.-J., Li, K., and Fei-Fei, L. (2009). Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition , pages 248--255. Ieee

    2009

  29. [37]

    Desai, A., Freeman, C., Wang, Z., and Beaver, I. (2021). TimeVAE : A Variational Auto - Encoder for Multivariate Time Series Generation . arXiv:2111.08095 [cs]

    2021 arXiv

  30. [38]

    W., and Engle, R

    Ding, Z., Granger, C. W., and Engle, R. F. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance , 1(1):83--106

    1993

  31. [39]

    A., Lamba, C., Kim, B., and Ionescu, B

    Dogariu, M., S tefan, L.-D., Boteanu, B. A., Lamba, C., Kim, B., and Ionescu, B. (2022). Generation of realistic synthetic financial time-series. ACM Trans. Multimedia Comput. Commun. Appl. , 18(4)

    2022

  32. [40]

    Eckerli, F. (2021). Generative Adversarial Networks in finance: an overview. SSRN Electronic Journal

    2021

  33. [41]

    Efron, B. (1994). Missing data, imputation, and the bootstrap. Journal of the American Statistical Association , 89(426):463--475

    1994

  34. [42]

    Ericson, L., Zhu, X., Han, X., Fu, R., Li, S., Guo, S., and Hu, P. (2024). Deep generative modeling for financial time series with application in var: A comparative review. arXiv preprint arXiv:2401.10370

    2024 arXiv

  35. [43]

    Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance , 25(2):383--417

    1970

  36. [44]

    Feizi, S., Farnia, F., Ginart, T., and Tse, D. (2017). Understanding gans: the lqg setting. arXiv preprint arXiv:1710.10793

    2017 arXiv

  37. [45]

    and Junike, G

    Flaig, S. and Junike, G. (2023). Validation of machine learning based scenario generators. arXiv:2301.12719 [q-fin]

    2023 arXiv

  38. [46]

    Fu, W., Hirsa, A., and Osterrieder, J. (2022). Simulating financial time series using attention. arXiv preprint arXiv:2207.00493

    2022 arXiv

  39. [47]

    Glasserman, P. (2004). Monte Carlo Methods in Financial Engineering , volume 53. Springer

    2004

  40. [48]

    Goerg, G. M. (2015). The lambert way to gaussianize heavy-tailed data with the inverse of tukey’sh transformation as a special case. The Scientific World Journal , 2015(1):909231

    2015

  41. [49]

    J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y

    Goodfellow, I. J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y. (2014). Generative Adversarial Networks . arXiv:1406.2661 [cs, stat]

    2014 arXiv

  42. [50]

    Hendrycks, D., Burns, C., Basart, S., Zou, A., Mazeika, M., Song, D., and Steinhardt, J. (2020). Measuring massive multitask language understanding. arXiv preprint arXiv:2009.03300

    2020 arXiv

  43. [51]

    Henry-Labordere, P. (2019). Generative models for financial data. Available at SSRN 3408007

    2019

  44. [52]

    Hertz, D. B. (1964). Risk analysis in capital investment. Harvard Business Review , 42:95--106

    1964

  45. [53]

    Hinton, G. E. and Sejnowski, T. J. (1983). Optimal perceptual inference. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition , volume 448, pages 448--453. Citeseer

    1983

  46. [54]

    Ho, J., Jain, A., and Abbeel, P. (2020). Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems , 33:6840--6851

    2020

  47. [55]

    Hoeffding, W. (1948). A Class of Statistics with Asymptotically Normal Distribution . The Annals of Mathematical Statistics , 19(3):293 -- 325

    1948

  48. [56]

    Hornik, K., Stinchcombe, M., and White, H. (1989). Multilayer feedforward networks are universal approximators. Neural networks , 2(5):359--366

    1989

  49. [57]

    M., and Pakkanen, M

    Horvath, B., Gonzalez, A. M., and Pakkanen, M. S. (2023). Harnessing quantitative finance by data-centric methods. Machine Learning and Data Sciences for Financial Markets: A Guide to Contemporary Practices , page 265

    2023

  50. [58]

    Issler, J. V. and Vahid, F. (1996). Common cycles in macroeconomic aggregates. mimeo

    1996

  51. [59]

    J \"a ckel, P. (2002). Monte Carlo Methods in Finance , volume 5. John Wiley & Sons

    2002

  52. [60]

    and Zhu, Y

    Jamshidian, F. and Zhu, Y. (1996). Scenario simulation: Theory and methodology. Finance and Stochastics , 1:43--67

    1996

  53. [61]

    and Boyd, M

    Kaastra, I. and Boyd, M. (1996). Designing a neural network for forecasting financial and economic time series. Neurocomputing , 10(3):215--236

    1996

  54. [62]

    Kantorovich, L. V. (1960). Mathematical methods of organizing and planning production. Management Science , 6(4):366--422

    1960

  55. [63]

    B., Chess, B., Child, R., Gray, S., Radford, A., Wu, J., and Amodei, D

    Kaplan, J., McCandlish, S., Henighan, T., Brown, T. B., Chess, B., Child, R., Gray, S., Radford, A., Wu, J., and Amodei, D. (2020). Scaling laws for neural language models. arXiv preprint arXiv:2001.08361

    2020 arXiv

  56. [64]

    Karras, T., Aittala, M., Hellsten, J., Laine, S., Lehtinen, J., and Aila, T. (2020). Training generative adversarial networks with limited data

    2020

  57. [65]

    Kim, Y., Kang, D., Jeon, M., and Lee, C. (2019). Gan-mp hybrid heuristic algorithm for non-convex portfolio optimization problem. The Engineering Economist , 64(3):196--226

    2019

  58. [66]

    Kingma, D. P. and Welling, M. (2013). Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114

    2013 arXiv

  59. [67]

    and Schwarz, C

    Kondratyev, A. and Schwarz, C. (2019). The Market Generator . SSRN Electronic Journal

    2019

  60. [68]

    Koshiyama, A., Firoozye, N., and Treleaven, P. (2019). Generative Adversarial Networks for Financial Trading Strategies Fine - Tuning and Combination . arXiv:1901.01751 [cs, q-fin, stat]

    2019 arXiv

  61. [69]

    and Wolf, M

    Ledoit, O. and Wolf, M. (2003). Honey, i shrunk the sample covariance matrix. UPF economics and business working paper

    2003

  62. [70]

    Lezmi, E., Roche, J., Roncalli, T., and Xu, J. (2020). Improving the Robustness of Trading Strategy Backtesting with Boltzmann Machines and Generative Adversarial Networks . SSRN Electronic Journal

    2020

  63. [71]

    and Xu, J

    Lezmi, E. and Xu, J. (2023). Time series forecasting with transformer models and application to asset management. Available at SSRN 4375798

    2023

  64. [72]

    Liao, S., Ni, H., Sabate-Vidales, M., Szpruch, L., Wiese, M., and Xiao, B. (2024). Sig-wasserstein gans for conditional time series generation. Mathematical Finance , 34(2):622--670

    2024

  65. [73]

    and Horvath, B

    Limmer, Y. and Horvath, B. (2023). Robust Hedging GANs . SSRN Electronic Journal

    2023

  66. [74]

    Lin, J. (1991). Divergence measures based on the shannon entropy. IEEE Transactions on Information Theory , 37(1):145--151

    1991

  67. [75]

    Lopez-Lira, A. (2019). Risk factors that matter: Textual analysis of risk disclosures for the cross-section of returns. Available at SSRN 3313663

    2019

  68. [76]

    Mandelbrot, B. B. (1997). The Variation of Certain Speculative Prices . Springer

    1997

  69. [77]

    Marchenko, V. A. and Pastur, L. A. (1967). Distribution of eigenvalues for some sets of random matrices. Matematicheskii Sbornik , 114(4):507--536

    1967

  70. [78]

    Mariani, G., Zhu, Y., Li, J., Scheidegger, F., Istrate, R., Bekas, C., and Malossi, A. C. I. (2019). Pagan: Portfolio analysis with generative adversarial networks. arXiv preprint arXiv:1909.10578

    2019 arXiv

  71. [79]

    Marti, G. (2020). Corrgan: Sampling realistic financial correlation matrices using generative adversarial networks. In ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) , pages 8459--8463. IEEE

    2020

  72. [80]

    Morel, R., Mallat, S., and Bouchaud, J.-P. (2023). Path Shadowing Monte - Carlo . arXiv:2308.01486 [q-fin]

    2023 arXiv

  73. [81]

    Nowozin, S., Cseke, B., and Tomioka, R. (2016). f-gan: Training generative neural samplers using variational divergence minimization. Advances in Neural Information Processing Systems , 29

    2016

  74. [82]

    Pardo, F. D. M. and L \'o pez, R. C. (2019). Mitigating overfitting on financial datasets with generative adversarial networks. The Journal of Financial Data Science

    2019

  75. [83]

    Parent, L. (2024). The factorial path-dependent market model. Available at SSRN 4855091

    2024

  76. [84]

    Peña, J.-M., Suárez, F., Larré, O., Ramírez, D., and Cifuentes, A. (2023). A Modified CTGAN - Plus - Features Based Method for Optimal Asset Allocation . arXiv:2302.02269 [cs, q-fin]

    2023 arXiv

  77. [85]

    Picci, G. (1977). Some connections between the theory of sufficient statistics and the identifiability problem. SIAM Journal on Applied Mathematics , 33(3):383--398

    1977

  78. [86]

    Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L. A. N., and Stanley, H. E. (1999). Universal and nonuniversal properties of cross correlations in financial time series. Physical Review Letters , 83(7):1471

    1999

  79. [87]

    K., Borrajo, D., Coletta, A., Dalmasso, N., El-Laham, Y., Fons, E., Ghassemi, M., Gopalakrishnan, S., Gosai, V., Krea c i \'c , E., et al

    Potluru, V. K., Borrajo, D., Coletta, A., Dalmasso, N., El-Laham, Y., Fons, E., Ghassemi, M., Gopalakrishnan, S., Gosai, V., Krea c i \'c , E., et al. (2023). Synthetic data applications in finance. arXiv preprint arXiv:2401.00081

    2023 arXiv

  80. [88]

    Ramesh, A., Dhariwal, P., Nichol, A., Chu, C., and Chen, M. (2022). Hierarchical text-conditional image generation with clip latents. arXiv preprint arXiv:2204.06125 , 1(2):3

    2022 arXiv

  81. [89]

    Rockafellar, R. T. and Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk , 2:21--42

    2000

  82. [90]

    Romer, C. D. (1999). Changes in business cycles: evidence and explanations. Journal of Economic Perspectives , 13(2):23--44

    1999

  83. [91]

    Rubin, D. B. (1976). Inference and missing data. Biometrika , 63(3):581--592

    1976

  84. [92]

    W., Prokhorov, D

    Saad, E. W., Prokhorov, D. V., and Wunsch, D. C. (1998). Comparative study of stock trend prediction using time delay, recurrent and probabilistic neural networks. IEEE Transactions on Neural Networks , 9(6):1456--1470

    1998

  85. [93]

    Sattarov, T., Schreyer, M., and Borth, D. (2023). Findiff: Diffusion models for financial tabular data generation. In Proceedings of the Fourth ACM International Conference on AI in Finance , pages 64--72

    2023

  86. [94]

    Seaman, S. R. and Vansteelandt, S. (2018). Introduction to double robust methods for incomplete data. Statistical science: a review journal of the Institute of Mathematical Statistics , 33(2):184

    2018

  87. [95]

    Serfling, R. J. (2009). Approximation Theorems of Mathematical Statistics . John Wiley & Sons

    2009

  88. [96]

    Shumailov, I., Shumaylov, Z., Zhao, Y., Papernot, N., Anderson, R., and Gal, Y. (2024). Ai models collapse when trained on recursively generated data. Nature , 631(8022):755--759

    2024

  89. [97]

    Sun, H., Deng, Z., Chen, H., and Parkes, D. (2023). Decision-aware conditional gans for time series data. In Proceedings of the Fourth ACM International Conference on AI in Finance , pages 36--45

    2023

  90. [98]

    Takahashi, S., Chen, Y., and Tanaka-Ishii, K. (2019). Modeling financial time-series with generative adversarial networks. Physica A: Statistical Mechanics and its Applications , 527:121261

    2019

  91. [99]

    van den Oord, A., Dieleman, S., Zen, H., Simonyan, K., Vinyals, O., Graves, A., Kalchbrenner, N., Senior, A., and Kavukcuoglu, K. (2016). Wavenet: A generative model for raw audio

    2016

  92. [100]

    and Cont, R

    Vuleti \'c , M. and Cont, R. (2023). Volgan: a generative model for arbitrage-free implied volatility surfaces. Available at SSRN

    2023

  93. [101]

    Vuletić, M., Prenzel, F., and Cucuringu, M. (2023). Fin- GAN : Forecasting and Classifying Financial Time Series via Generative Adversarial Networks . SSRN Electronic Journal

    2023

  94. [102]

    and Robins, J

    Wang, N. and Robins, J. M. (1998). Large-sample theory for parametric multiple imputation procedures. Biometrika , 85(4):935--948

    1998

  95. [103]

    Wiese, M., Bai, L., Wood, B., and Buehler, H. (2019). Deep hedging: learning to simulate equity option markets. arXiv preprint arXiv:1911.01700

    2019 arXiv

  96. [104]

    Wiese, M., Knobloch, R., Korn, R., and Kretschmer, P. (2020). Quant GANs : Deep Generation of Financial Time Series . Quantitative Finance , 20(9):1419--1440. arXiv:1907.06673 [cs, q-fin, stat]

    2020 arXiv

  97. [105]

    Wolpert, D. H. (1996). The lack of a priori distinctions between learning algorithms. Neural Computation , 8(7):1341--1390

    1996

  98. [106]

    and Papanicolaou, G

    Yeo, J. and Papanicolaou, G. (2017). Risk control of mean-reversion time in statistical arbitrage. Risk and Decision Analysis , 6(4):263--290

    2017

  99. [107]

    Yoon, J., Jarrett, D., and van der Schaar, M. (2019). Time-series Generative Adversarial Networks . In Advances in Neural Information Processing Systems , volume 32. Curran Associates, Inc

    2019

  100. [108]

    Zhang, J., Qiao, D., Yang, M., and Wei, Q. (2024). Regurgitative training: The value of real data in training large language models. arXiv preprint arXiv:2407.12835

    2024 arXiv

  101. [109]

    Zumbach, G. (2007). Time reversal invariance in finance. arXiv:0708.4022 [physics, q-fin]

    2007 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.