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arxiv: 1906.09632 · v1 · pith:K4JCWIWWnew · submitted 2019-06-23 · 💻 cs.CY · q-fin.RM· q-fin.ST

A Model of the Optimal Selection of Crypto Assets

Silvia Bartolucci , Andrei Kirilenko This is my paper

Pith reviewed 2026-05-25 17:38 UTC · model grok-4.3

classification 💻 cs.CY q-fin.RMq-fin.ST
keywords crypto assetsoptimal selectionsecurity and stabilitypairwise comparisonsrecommender modelinvestor attitudesemergent outcomessimulation
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The pith

Investors reach optimal crypto selections by comparing asset pairs until expected economic benefits stop improving.

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

The paper presents a framework in which crypto assets are distinguished by security and stability features. Investors evaluate pairs of assets through a process modeled on a recommender app that weighs those features, the choices of other investors, and projected future benefits. They keep making pairwise adoption decisions across all possible pairs until further changes yield no additional expected benefit. Simulations that vary investor attitudes toward the two features produce multiple distinct patterns of asset adoption and investment allocation in the broader crypto ecosystem.

Core claim

Investors reach an optimal selection decision by continuing to compare pairs of crypto assets until their expected future economic benefits can no longer be improved upon. The model treats the comparison process as guided by an app that incorporates each asset's security-stability profile, aggregate adoption information from other investors, and benefit projections, with simulations showing that different investor preference types generate varied emergent investment outcomes.

What carries the argument

The recommender-app comparison process that presents asset pairs and recommends adoptions based on security-stability features, collective choices, and expected benefits until no further improvement is possible.

If this is right

  • Optimal selections emerge from the interaction between security and stability attributes across the full set of assets.
  • Different investor types, defined by their weighting of features, produce distinct patterns of asset holdings.
  • The process converges to a stable allocation once pairwise improvements are exhausted.
  • Collective adoption data influences individual recommendations and therefore shapes the final portfolio.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The framework implies that providing investors with accurate information on others' choices could accelerate convergence to certain asset sets.
  • It could be extended to test whether adding network effects or liquidity constraints changes which allocations count as optimal.
  • The model suggests that policy interventions altering perceived stability might shift the entire distribution of simulated outcomes.
  • Real-time data on pairwise comparison activity might serve as an early indicator of which assets are approaching adoption saturation.

Load-bearing premise

The recommender app can correctly judge whether an adoption improves expected benefits and investors will keep comparing pairs until no further gains remain available.

What would settle it

Track whether actual crypto investors cease changing their holdings once information on others' choices and benefit projections indicates no further expected improvement, or check whether simulated adoption patterns under different preference types match observed market distributions.

Figures

Figures reproduced from arXiv: 1906.09632 by Andrei Kirilenko, Silvia Bartolucci.

Figure 1
Figure 1. Figure 1: Scheme of the main components of the optimal selection model. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic representation of the crypto assets dynamics. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Top: Optimal assets selection outcome in the adoption-expected return space. Simulation with [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Optimal assets selection outcome in the adoption-expected return space. Simulation with [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Total expected return in time for different [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Optimal assets selection outcome in the adoption-expected return space. Simulation with [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Optimal assets selection outcome in the adoption-expected return space. Simulation with [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Phase diagram of the system varying the parameters [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Numerical estimation of β 0 as a function of β according to Eq. (14), given π 0 (s), πˆ 0 (ξ) uniform and (i) π(s) = 1, πˆ(ξ) = 1 (uniform pdf with s, ξ ∈ [0, 1]) and (ii) π(s) = 2s, πˆ(ξ) = 2ξ (triangular pdf with s, ξ ∈ [0, 1]). Therefore, we simulate a system with π(s) = ˆπ(ξ) = 1 uniform between [0, 1] and one where the features are extracted from a triangular pdf in [0, 1]: π(s) = 2s, πˆ(ξ) = 2ξ. In … view at source ↗
Figure 10
Figure 10. Figure 10: Mean (and variance) of the probability of not being adopted per asset class for the following scenario [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Simulation with N = 200 crypto assets, δ = 0.1 and ns = 300. Top: Optimal assets selection outcome in the adoption-expected return space for the case of heterogeneous investors (left) and homogeneous investors with hβ1i = 1.234 and hβ2i = 1.549 (right). Bottom: Distribution of mean probability of not being adopted 1 − a, conditioned on the assets’ class χ, P(1 − a|χ) for the heterogeneous (left) and homog… view at source ↗
read the original abstract

We propose a modelling framework for the optimal selection of crypto assets. Crypto assets differ by two essential features: security (technological) and stability (governance). Investors make choices over crypto assets similarly to how they make choices by using a recommender app: the app presents each investor with a pair of crypto assets with certain security-stability characteristics to be compared. Each investor submits its preference for adopting one of the two assets to the app. The app, in turn, provides a recommendation on whether the proposed adoption is sensible given the assets' essential features, information about the adoption choices of all other investors, and expected future economic benefits of adoption. Investors continue making their adoption choices over all pairs of crypto assets until their expected future economic benefits can no longer be improved upon. This constitutes an optimal selection decision. We simulate optimal selection decisions considering the behaviour of different types of investors, driven by their attitudes towards assets' features. We find a variety of possible emergent outcomes for the investments in the crypto-ecosystem and the future adoption of the crypto assets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper proposes a modeling framework for the optimal selection of crypto assets that differ in security (technological) and stability (governance) features. Investors compare asset pairs via a recommender app that incorporates asset features, other investors' adoption choices, and expected future economic benefits; pairwise choices continue until no further improvement in expected benefits is possible, which the paper asserts constitutes an optimal selection. Simulations across investor types (differing in attitudes toward features) are said to produce a variety of emergent outcomes for the crypto ecosystem.

Significance. If the optimality claim were formally derived and the simulations were reproducible with explicit utility functions and convergence conditions, the framework could contribute to agent-based modeling of technology adoption in decentralized systems. However, the absence of any such formalization means the work does not yet deliver a testable or derivable result.

major comments (2)
  1. [Abstract] Abstract: the central claim that repeated pairwise comparisons 'constitute an optimal selection decision' is unsupported; no utility function, no expression for 'expected future economic benefits,' no aggregation rule across investors, and no argument establishing that the described process reaches a fixed point or global optimum are supplied.
  2. [Abstract] Abstract: the statement that 'simulations ... produce a variety of possible emergent outcomes' cannot be evaluated because the manuscript provides neither the model equations, the recommender logic, the investor-type parameterizations, nor any stopping rule or validation procedure.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for highlighting issues in the abstract. The manuscript presents a conceptual framework rather than a fully formalized mathematical model with explicit proofs. We will revise the abstract for clarity and precision on the claims made, while noting that the core contribution is the iterative preference process and simulation outcomes. No standing objections beyond what is addressed below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that repeated pairwise comparisons 'constitute an optimal selection decision' is unsupported; no utility function, no expression for 'expected future economic benefits,' no aggregation rule across investors, and no argument establishing that the described process reaches a fixed point or global optimum are supplied.

    Authors: We agree the abstract overstates the claim without supporting detail. The described process defines optimality locally as the point where no further pairwise improvement in expected benefits is possible, drawing on recommender-style iteration with network effects from other investors. This is not asserted as a proven global optimum. We will revise the abstract to qualify the claim as a local equilibrium reached via iterative pairwise choices and add a brief note on the implicit utility (security-stability features plus adoption externalities). revision: yes

  2. Referee: [Abstract] Abstract: the statement that 'simulations ... produce a variety of possible emergent outcomes' cannot be evaluated because the manuscript provides neither the model equations, the recommender logic, the investor-type parameterizations, nor any stopping rule or validation procedure.

    Authors: The full manuscript describes the recommender logic (pairwise feature comparison incorporating other investors' choices and benefits), investor types (parameterized by attitudes to security vs. stability), and stopping when no improvement occurs. However, the abstract is too terse to convey this. We will revise the abstract to reference the simulation parameterization and emergent outcomes more explicitly, and ensure the main text highlights the equations and convergence rule if not already prominent. revision: yes

Circularity Check

1 steps flagged

Optimality of selection process asserted by equating it to the stopping condition of pairwise comparisons

specific steps
  1. self definitional [Abstract]
    "Investors continue making their adoption choices over all pairs of crypto assets until their expected future economic benefits can no longer be improved upon. This constitutes an optimal selection decision."

    The text defines the iterative pairwise process and its stopping condition, then directly states that this stopping point 'constitutes an optimal selection decision.' Optimality is therefore true by the construction of the stopping rule rather than derived from independent premises such as a utility function or global optimization argument.

full rationale

The paper's central claim equates the described tâtonnement process to optimality solely via the stopping rule of no further improvement in expected benefits. This is self-definitional rather than derived from an explicit utility function, equilibrium condition, or convergence proof. No equations, self-citations, or fitted-parameter predictions appear in the provided text to create additional circular reductions. The simulation outcomes are presented as emergent from investor types but are not shown to be forced by the optimality definition itself.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available. No free parameters, axioms, or invented entities are specified in the provided text. The framework appears to rely on unstated assumptions about how the recommender app computes recommendations and how investor types are parameterized, but these cannot be enumerated.

pith-pipeline@v0.9.0 · 5713 in / 1241 out tokens · 29857 ms · 2026-05-25T17:38:45.731556+00:00 · methodology

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Reference graph

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