Betting vs. Trading: Learning a Linear Decision Policy for Selling Wind Power and Hydrogen

Farzaneh Pourahmadi; Jalal Kazempour; Yannick Heiser

REVIEW 3 major objections 4 minor 16 references

Betting vs. Trading: Learning a Linear Decision Policy for Selling Wind Power and Hydrogen

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Enforcing explicit caps on imbalance size converts the all-or-nothing betting strategy that single imbalance pricing invites into a diversified trading strategy for a wind-plus-hydrogen plant, recovering 50–83% of perfect-foresight profit.

desk verdict A plausible and well-presented method for diversifying day-ahead trading under single imbalance pricing, but missing CVaR alpha and no out-of-sample verification of risk constraints. read the letter →

arxiv 2412.18479 v2 pith:745KR4FE submitted 2024-12-24 eess.SY cs.SY

Yannick Heiser , Farzaneh Pourahmadi , Jalal Kazempour This is my paper · ORCID

classification eess.SYcs.SY

keywords singleimbalancepricebettingstrategytradinglineardecisionpolicywindpowerhydrogenelectrolyzerday-aheadelectricitymarket

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

The paper tries to establish that a wind-plus-hydrogen plant selling into a day-ahead market with single imbalance pricing will, if it only maximizes expected profit, end up betting everything on one market being more expensive than the other: selling full capacity day-ahead or nothing at all. That all-or-nothing behavior is risky because it requires predicting the direction of system imbalance, which is a hard forecasting task. The paper's proposal is to add explicit caps on the allowed size of the imbalance (its mean, its CVaR, or its maximum) to a data-driven linear decision policy, which converts the binary bet into a diversified trading curve while still scheduling hydrogen production. In a 2019-train/2020-test case study, the risk-constrained policies reach 50–83% of the profit a perfect-foresight oracle would earn, with the higher numbers when hydrogen prices make the operational choice simpler. The practical point is that a simple, transparent linear policy plus a risk cap may be enough to operate safely under single imbalance pricing without elaborate forecasting.

What carries the argument

The machinery is a set of linear decision policies $q^{DA}_{j,k}$ and $q^{H}_{j,k}$ that map a feature vector $x_t=(\hat{\lambda}^{DA}_t,\tilde{\lambda}^{DA}_t,\tilde{P}^W_t,1)$ to the day-ahead power bid $p^{DA}_t$ and the electrolyzer consumption $p^{H}_t$, for each hour-of-day $j$ and price domain $k$. Because the realized day-ahead price is the first feature, each policy defines an affine bidding curve $p^{DA}=a_1\lambda^{DA}+b_1$; constraints keep the curve non-decreasing across price domains. The second piece is the risk constraint on the auxiliary variable $\Delta p^{ABS}_t\geq |\Delta p_t|$, either the mean bound $\frac{1}{|H|}\sum_t \Delta p^{ABS}_t \leq \Delta P^{\mathrm{mean}}$, the CVaR bound $\mathrm{VaR}+\frac{1}{(1-\alpha)|H|}\sum_t \xi_t \leq \Delta P^{\mathrm{CVaR}}$, or the extreme bound $\Delta p^{ABS}_t\leq \Delta P^{\mathrm{ext}}$. These caps on imbalance are what force diversification away from the binary all-or-nothing outcome.

What would settle it

If an out-of-sample test with a policy trained on one year and tested on a different year showed the realized day-ahead trades still clustered at the maximum buy and sell quantities (for example, more than 90% of trades within 1% of the capacity limits) or the profit ratio fell to that of the unconstrained betting model, the claim that risk constraints convert betting to trading would be falsified.

Watch

Extended reading notes

Core claim

Under single imbalance pricing, a profit-maximizing producer without risk constraints commits all-or-nothing in the day-ahead market because the optimal action is to sell everything if the day-ahead price is expected to exceed the balancing price and sell nothing otherwise. The paper's central discovery is that this binary behavior disappears when the optimization explicitly constrains the magnitude of the power imbalance settled in the balancing market: bounding the mean, the CVaR, or the maximum absolute imbalance forces the linear decision policy to spread sales across quantities instead of collapsing to the extremes. The resulting trading model produces a non-decreasing price-quantity bidding curve and a hydrogen schedule, and in the tested 2020 out-of-sample period it delivers profit ratios around 0.79–0.83 depending on grid-purchase restrictions, and 0.50–0.83 across hydrogen prices, compared with a perfect-foresight oracle.

Load-bearing premise

The approach assumes that correcting an infeasible bidding curve by projecting it onto the nearest feasible curve, using risk limits tuned on one year of data, yields decisions close to the true optimal feasible policy in the next year.

Editorial extensions

If this is right

A plant operator can train a linear policy on one year of historical features (forecast price, forecast wind, realized day-ahead price) and then use it to construct and submit a monotone price-quantity curve without solving the stochastic optimization online.
The risk cap can be tuned to the operator's risk appetite: setting the CVaR limit to 30% or 50% of the unconstrained betting model's CVaR produces visibly more diversified realized day-ahead trades.
Because mean, CVaR, and extreme caps give profit ratios within 0.5% of each other, an operator can pick the simplest constraint to implement without much loss.
Restricting grid purchases for green-hydrogen certification costs little: sell-only models reach about 0.79 of oracle profit versus about 0.83 for unrestricted buying under the tested conditions.
Higher hydrogen prices simplify the operational choice (run the electrolyzer at capacity), raising the profit ratio from about 0.5 at €2/kg to 0.83 at €6/kg.

Reading between the lines

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

The betting pathology is a property of the single imbalance pricing rule, not of wind or hydrogen specifically, so the same cap-on-imbalance idea should apply to any price-taking participant in such a market; the paper only demonstrates it for this hybrid plant.
A continuous sweep of the risk cap should reveal a phase transition in the realized trade distribution, from binary at no cap to dispersed at tight cap; the paper shows only fixed calibrations, so such a sweep would be a direct test of the mechanism.
The near-equivalence of the mean, CVaR, and extreme constraints hints that the binding feature is overall tail exposure rather than the specific risk measure, so a single quantile constraint might reproduce the same behavior at lower computational cost; this is not tested in the paper.
The 50%-of-betting-CVaR calibration was chosen on the training year, so a natural extension is to check whether that calibration remains stable across years or requires periodic recalibration.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Dear colleague,

Two things to know about this paper. The central idea—using explicit risk constraints on imbalance magnitude to break the all-or-nothing bidding pattern under single imbalance pricing—is plausible, and the out-of-sample comparison against a perfect-foresight oracle is a reasonable way to test it. But the paper never verifies that the risk constraints actually bind out-of-sample, and the CVaR confidence level alpha in equation (9a) is never specified. Those are the soft spots that matter most.

What is genuinely new is the combination: linear decision policies for a wind-electrolyzer plant, with three types of risk constraints (mean, CVaR, extreme) that convert binary bets into diversified trades. The LP and MILP formulations are clearly stated and follow standard practice. The authors are transparent that the building blocks come from existing work—linear decision rules, CVaR, and the hybrid plant model—and their contribution is the specific combination plus the risk-constraint mechanism. The reported profit ratios (0.5 to 0.83 of the oracle) are encouraging for a simple, transparent method, and the realized trade distributions in Fig. 3b do support the qualitative claim that risk constraints diversify decisions.

Now the soft spots, in proportion. The missing alpha is a straightforward replication blocker; it needs to be stated. More seriously, the risk constraints are only enforced in training. At test time, the policies go through a feasibility-restoration step, but the paper never reports whether the realized 2020 imbalances actually respect the limits set by the calibrated parameters. If test-period imbalance risk exceeds those limits, then the observed diversification could be driven by the projection heuristic or hydrogen-price economics rather than by the risk constraints—which would undermine the paper's central claim. This is not a fatal flaw, but it is a real gap. The feasibility-restoration step itself is only described qualitatively; there is no evidence that the projection is close to the optimal feasible policy. The risk limits are hand-picked fractions (30% or 50%) of the betting model's own metrics from 2019, with no sensitivity analysis. The code link appears to have a typo, and there are no comparisons to established baselines like the newsvendor approach or the dual-pricing model of [10]. The 'first work' claim in Section 1 also overreaches relative to [9], which already considers risk-constrained trading under a single-price balancing market; the authors need to sharpen the distinction.

Overall, this is a solid applied paper with a clear method and a sensible evaluation. The single synthetic case study limits generalizability, but the qualitative finding is credible. Researchers working on bidding strategies for renewables or hybrid plants should read it. It deserves a serious referee, and I would send it to peer review with the request that the authors add the missing alpha, an out-of-sample check of the risk constraints, and some validation of the projection step.

Referee Report

3 major / 4 minor

Summary. The paper develops linear decision policies for a co-located wind-electrolyzer hybrid plant bidding into a day-ahead market under single imbalance pricing. Without risk management, the optimal policy is all-or-nothing ('betting'); the authors propose explicit constraints on the mean, CVaR, and maximum absolute imbalance to obtain a diversified 'trading' strategy. The training models are linear programs (or MILPs for conditional grid purchase), the testing phase constructs bidding curves from a subset of features and applies a feasibility-restoration projection, and the approach is evaluated on synthetic 2019/2020 data against a perfect-foresight oracle under three grid-purchase regimes.

Significance. If the central claim holds, the paper offers a simple and practical mechanism for avoiding the degenerate all-or-nothing behavior known under single imbalance pricing, and it does so with a transparent data-driven formulation. The models are clearly stated, the code is publicly available, and the comparison to a hindsight oracle is an honest way of quantifying the cost of learning. The main value is in showing that a direct risk constraint, rather than a risk-adjusted objective, can restore diversified trading behavior. However, the numerical evidence currently does not establish that the risk constraints remain effective out of sample, which is essential for the claimed mechanism.

major comments (3)

[Section 4.2 and Section 5.3] The risk constraints (8)-(10) are enforced only on the 2019 training sample, where the policies are fitted. At test time, the feasibility-restoration step in Section 4.2 corrects monotonicity and bounds but does not enforce the imbalance limits, and the paper does not report the realized mean absolute imbalance, CVaR, or maximum absolute imbalance for the 2020 test set. Since the central claim is that these constraints transform betting into trading, the paper needs to show out-of-sample imbalance metrics against the calibrated limits (30% or 50% of the betting model's values). Without this, the diversification visible in Fig. 3b and the profit ratios in Fig. 5 cannot be attributed specifically to the risk constraints rather than to the projection heuristic or to hydrogen-price economics.
[Section 3.4, Eq. (9a)] The CVaR confidence level alpha in Eq. (9a) is never specified. The value of alpha directly changes the CVaR constraint and therefore the resulting trading policy; omitting it makes the results for TCVaR non-reproducible and prevents a meaningful comparison of the three risk-constraint types in Fig. 5. Please state alpha and provide a sensitivity analysis over reasonable values.
[Section 4.2] The feasibility-restoration step is a greedy projection of the learned bidding curve onto a feasible region. The paper gives no quantitative evidence that this projection is close to the true optimal feasible policy: it does not report how often the monotonicity or bound constraints are violated, how large the resulting curve modification is, or whether a feasible re-optimization would give materially different profits. Since the reported testing profits are computed after this heuristic step, the profit ratios in Fig. 4 and Fig. 5 could be affected by projection error. Please provide statistics on the projection and, if possible, compare against an exact feasibility-restoration formulation.

minor comments (4)

[Section 3.3] There is a duplicated phrase in the sentence 'The objective function The objective function (3a) incorporates...' that should be corrected.
[Section 5.1] The text says Fig. 3a and Fig. 3b show trades 'during the training period, which covers all hours of 2020', but the models are trained on 2019 and tested on 2020; this should be 'testing period'.
[Section 5.1 and Fig. 3] The narrative refers to hindsight plots both as 'Fig. 3d and Fig. 3e' and as 'plots (c) and (d)', which is inconsistent; please align the text with the panel labels in the figure.
[Section 5.3] The choice of 50% (and 30% in Section 5.1) of the betting model's risk values as the constraint limits is not justified. A short discussion of how the results depend on this fraction would strengthen the claim that the diversification is a robust property of risk-constrained policies.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central betting-to-trading claim is evaluated out-of-sample against a perfect-foresight oracle, and the risk-limit calibration is an input choice, not a fitted prediction.

full rationale

I examined the full derivation chain. The linear policies in (2) are fitted on the 2019 training sample; the risk constraints (8)-(10) are imposed only in the training LP (Section 3.4), and the testing phase (Section 4.1) fixes the trained policies and evaluates them on 2020 realizations after a feasibility-restoration heuristic (Section 4.2). The reported performance metric is the profit ratio against a perfect-foresight oracle, an external benchmark, so the central performance claim is not an in-sample artifact. The risk limits are chosen as fixed fractions of the unconstrained betting model's own imbalance statistics: '30% of the CVaR value obtained from the optimal solution of the betting model' (Section 5.1) and '50% of their corresponding values in the unconstrained betting model, B' (Section 5.3). These are hand-picked calibration constants, not parameters fitted to the test data and then renamed as predictions; the paper never claims to forecast the out-of-sample risk metrics. The diversification in Fig. 3b is a realized out-of-sample distribution of day-ahead trades, not a constraint-enforced training output, and no equation in the model defines 'trading' in terms of the test-period satisfaction of the risk limits. Self-citations [10] and [12] supply the synthetic data and the electrolyzer outer-approximation linearization; they are used as modeling building blocks, not as the justification for the betting-to-trading transformation, and neither is invoked as a uniqueness theorem. The skeptic's concern that the 2020 test period may violate the calibrated risk limits is a correctness/validation question, not a circularity, because the paper does not define its conclusion as the satisfaction of those limits. I therefore find no step in which a prediction reduces by construction to a fitted input or a self-citation chain.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The free parameters are calibration choices for the policy family and risk limits, plus an unspecified alpha. The axioms are standard domain assumptions plus one ad hoc heuristic. No new physical entities are introduced.

free parameters (3)

Price domain boundaries for |K|=10 = 10% quantiles of historic day-ahead prices
Chosen as hyperparameters in Section 5; they define the piecewise linear bidding curve and affect policy flexibility.
Risk limit fractions (CVaR, mean, extreme) = 30% (Section 5.1) and 50% (Section 5.3) of the betting model's corresponding values
Hand-picked to demonstrate diversification; no principled selection method is given.
CVaR confidence level alpha = Not specified in the text
Equation (9a) includes alpha but no value is reported, leaving the risk model incompletely specified.

assumptions (4)

domain assumption The linear outer approximation of the electrolyzer's non-convex production curve is exact for the operating conditions considered.
Invoked in Section 2 with reference [12]; if the relaxation is not exact, the hydrogen schedule may be infeasible or suboptimal.
domain assumption The synthetic data from [10] based on Roedsand and Energinet is representative of real market conditions for evaluating out-of-sample performance.
Section 5 states all data is synthetic; the generalization of the results depends on this.
standard math Single imbalance pricing creates an arbitrage opportunity such that the unconstrained optimum is all-or-nothing.
Used throughout, e.g., Section 1 and Section 3.3; this is the premise that motivates the risk constraints.
ad hoc to paper The greedy feasibility restoration projection in Section 4.2 results in a near-optimal feasible solution.
No theoretical or numerical analysis of the projection error is provided; the reported testing profits depend on this heuristic.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Betting vs. Trading: Learning a Linear Decision Policy for Selling Wind Power and Hydrogen." pith.science (2026). https://pith.science/paper/745KR4FE

@misc{pith2026241218479,
  author       = {Pith},
  title        = {Pith review of: Betting vs. Trading: Learning a Linear Decision Policy for Selling Wind Power and Hydrogen},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/745KR4FE}},
  note         = {Machine review of arXiv:2412.18479}
}

read the original abstract

We develop a bidding strategy for a hybrid power plant combining co-located wind turbines and an electrolyzer, constructing a price-quantity bidding curve for the day-ahead electricity market while optimally scheduling hydrogen production. Without risk management, single imbalance pricing leads to an all-or-nothing trading strategy, which we term 'betting'. To address this, we propose a data-driven, pragmatic approach that leverages contextual information to train linear decision policies for both power bidding and hydrogen scheduling. By introducing explicit risk constraints to limit imbalances, we move from the all-or-nothing approach to a 'trading" strategy', where the plant diversifies its power trading decisions. We evaluate the model under three scenarios: when the plant is either conditionally allowed, always allowed, or not allowed to buy power from the grid, which impacts the green certification of the hydrogen produced. Comparing our data-driven strategy with an oracle model that has perfect foresight, we show that the risk-constrained, data-driven approach delivers satisfactory performance.

Figures

Figures reproduced from arXiv: 2412.18479 by the authors.

**Figure 2.** Bidding curve examples: Plot (a) illustrates the transition from one price domain [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** The distribution of realized hourly trades [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Impact of hydrogen price on the profit obtained in both the training [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Comparison of all nine trading models in terms of their profit during [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

16 extracted references · 15 canonical work pages

[10]

Feature-driven strategies for trading wind power and hydrogen,

E. Helgren, J. Kazempour, and L. Mitridati, “Feature-driven strategies for trading wind power and hydrogen,”Electric Power Systems Research, vol. 234, p. 110787, 2024

work page 2024
[9]

Risk constrained trading strategies for stochastic generation with a single-price balancing market,

J. Browell, “Risk constrained trading strategies for stochastic generation with a single-price balancing market,” Energies, vol. 11, no. 6, p. 1345, 2018

work page 2018
[1]

Trading wind gen- eration from short-term probabilistic forecasts of wind power,

P. Pinson, C. Chevallier, and G. N. Kariniotakis, “Trading wind gen- eration from short-term probabilistic forecasts of wind power,” IEEE Transactions on Power Systems , vol. 22, no. 3, pp. 1148–1156, 2007

work page 2007
[2]

Short-term trading for a wind power producer,

J. M. Morales, A. J. Conejo, and J. Perez-Ruiz, “Short-term trading for a wind power producer,” IEEE Transactions on Power Systems, vol. 25, no. 1, pp. 554–564, 2010

work page 2010
[3]

X. A. Sun and A. J. Conejo, Robust Optimization in Short-Term Power System Operations. Cham: Springer International Publishing, 2021, pp. 239–279

work page 2021
[4]

Distributionally robust trading strategies for renewable energy producers,

P. Pinson, “Distributionally robust trading strategies for renewable energy producers,” IEEE Transactions on Energy Markets, Policy and Regulation, vol. 1, no. 1, pp. 37–47, 2023

work page 2023
[5]

Feature-driven improve- ment of renewable energy forecasting and trading,

M. A. Mu ˜noz, J. M. Morales, and S. Pineda, “Feature-driven improve- ment of renewable energy forecasting and trading,” IEEE Transactions on Power Systems, vol. 35, no. 5, pp. 3753–3763, 2020

work page 2020
[6]

Online decision making for trading wind energy,

M. Mu ˜noz, P. Pinson, and J. Kazempour, “Online decision making for trading wind energy,” Computational Management Science , vol. 20, p. 33, 2023

work page 2023

Show all 16 references

[7]

Commission regulation (EU) 2017/2195 of 23 November 2017 es- tablishing a guideline on electricity balancing,

“Commission regulation (EU) 2017/2195 of 23 November 2017 es- tablishing a guideline on electricity balancing,” https://eur-lex.europa. eu/legal-content/EN/TXT/?uri=CELEX%3A32017R2195, 2017, official Journal of the European Union, L 312, 28.11.2017, p. 6-53

2017
[8]

Optimization of conditional value-at- risk,

R. T. Rockafellar and S. Uryasev, “Optimization of conditional value-at- risk,” Journal of Risk , vol. 2, pp. 21–41, 2000

2000
[11]

Primal and dual linear decision rules in stochastic and robust optimization,

D. Kuhn, W. Wiesemann, and Georghiou, “Primal and dual linear decision rules in stochastic and robust optimization,” Mathematical Programming, vol. 130, p. 177–209, 2011

2011
[12]

A conic model for electrolyzer scheduling,

E. Raheli, Y . Werner, and J. Kazempour, “A conic model for electrolyzer scheduling,” Computers & Chemical Engineering , vol. 179, p. 108450, 2023

2023
[13]

EU Rules for Renewable Hydrogen—delegated regulations on a methodology for renewable fuels of non-biological origin,

“EU Rules for Renewable Hydrogen—delegated regulations on a methodology for renewable fuels of non-biological origin,” https://www.europarl.europa.eu/RegData/etudes/BRIE/2023/747085/ EPRS BRI(2023)747085 EN.pdf, 2023

2023
[14]

A survey of contextual optimization methods for decision-making under uncertainty,

U. Sadana, A. Chenreddy, E. Delage, A. Forel, E. Frejinger, and T. Vidal, “A survey of contextual optimization methods for decision-making under uncertainty,”European Journal of Operational Research, vol. 320, no. 2, pp. 271–289, 2025

2025
[15]

betting vs trading,

“betting vs trading,” https://github.com/yahei-DTU/betting vs trading, 2024

2024
[16]

Regression equilibrium in electricity markets,

V . Dvorkin, “Regression equilibrium in electricity markets,”IEEE Trans- actions on Energy Markets, Policy and Regulation , vol. 3, no. 1, pp. 121–132, 2025

2025

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [10]

Feature-driven strategies for trading wind power and hydrogen,

E. Helgren, J. Kazempour, and L. Mitridati, “Feature-driven strategies for trading wind power and hydrogen,”Electric Power Systems Research, vol. 234, p. 110787, 2024

work page 2024

[2] [9]

Risk constrained trading strategies for stochastic generation with a single-price balancing market,

J. Browell, “Risk constrained trading strategies for stochastic generation with a single-price balancing market,” Energies, vol. 11, no. 6, p. 1345, 2018

work page 2018

[3] [1]

Trading wind gen- eration from short-term probabilistic forecasts of wind power,

P. Pinson, C. Chevallier, and G. N. Kariniotakis, “Trading wind gen- eration from short-term probabilistic forecasts of wind power,” IEEE Transactions on Power Systems , vol. 22, no. 3, pp. 1148–1156, 2007

work page 2007

[4] [2]

Short-term trading for a wind power producer,

J. M. Morales, A. J. Conejo, and J. Perez-Ruiz, “Short-term trading for a wind power producer,” IEEE Transactions on Power Systems, vol. 25, no. 1, pp. 554–564, 2010

work page 2010

[5] [3]

X. A. Sun and A. J. Conejo, Robust Optimization in Short-Term Power System Operations. Cham: Springer International Publishing, 2021, pp. 239–279

work page 2021

[6] [4]

Distributionally robust trading strategies for renewable energy producers,

P. Pinson, “Distributionally robust trading strategies for renewable energy producers,” IEEE Transactions on Energy Markets, Policy and Regulation, vol. 1, no. 1, pp. 37–47, 2023

work page 2023

[7] [5]

Feature-driven improve- ment of renewable energy forecasting and trading,

M. A. Mu ˜noz, J. M. Morales, and S. Pineda, “Feature-driven improve- ment of renewable energy forecasting and trading,” IEEE Transactions on Power Systems, vol. 35, no. 5, pp. 3753–3763, 2020

work page 2020

[8] [6]

Online decision making for trading wind energy,

M. Mu ˜noz, P. Pinson, and J. Kazempour, “Online decision making for trading wind energy,” Computational Management Science , vol. 20, p. 33, 2023

work page 2023