Competition and Incentives in a Shared Order Book ArXiv ID: 2509.10094 “View on arXiv” Authors: René Aïd, Philippe Bergault, Mathieu Rosenbaum Abstract Recent regulation on intraday electricity markets has led to the development of shared order books with the intention to foster competition and increase market liquidity. In this paper, we address the question of the efficiency of such regulations by analysing the situation of two exchanges sharing a single limit order book, i.e. a quote by a market maker can be hit by a trade arriving on the other exchange. We develop a Principal-Agent model where each exchange acts as the Principal of her own market maker acting as her Agent. Exchanges and market makers have all CARA utility functions with potentially different risk-aversion parameters. In terms of mathematical result, we show existence and uniqueness of the resulting Nash equilibrium between exchanges, give the optimal incentive contracts and provide numerical solution to the PDE satisfied by the certainty equivalent of the exchanges. From an economic standpoint, our model demonstrates that incentive provision constitutes a public good. More precisely, it highlights the presence of a competitiveness spillover effect: when one exchange optimally incentivizes its market maker, the competing exchange also reaps indirect benefits. This interdependence gives rise to a free-rider problem. Given that providing incentives entails a cost, the strategic interaction between exchanges may lead to an equilibrium in which neither platform offers incentives – ultimately resulting in diminished overall competition. ...

Optimized Operation of Standalone Battery Energy Storage Systems in the Cross-Market Energy Arbitrage Business ArXiv ID: 2509.21337 “View on arXiv” Authors: Luis van Sandbergen Abstract The provision of renewable electricity is the foundation for a sustainable future. To achieve the goal of sustainable renewable energy, Battery Energy Storage Systems (BESS) could play a key role to counteract the intermittency of solar and wind generation power. In order to aid the system, the BESS can simply charge at low wholesale prices and discharge during high prices, which is also called energy arbitrage. However, the real-time execution of energy arbitrage is not straightforward for many companies due to the fundamentally different behavior of storages compared to conventional power plants. In this work, the optimized operation of standalone BESS in the cross-market energy arbitrage business is addressed by describing a generic framework for trading integrated BESS operation, the development of a suitable backtest engine and a specific optimization-based strategy formulation for cross-market optimized BESS operation. In addition, this strategy is tested in a case study with a sensitivity analysis to investigate the influence of forecast uncertainty. The results show that the proposed strategy allows an increment in revenues by taking advantage of the increasing market volatility. Furthermore, the sensitivity analysis shows the robustness of the proposed strategy, as only a moderate portion of revenues will be lost if real forecasts are adopted. ...

The Interplay between Utility and Risk in Portfolio Selection ArXiv ID: 2509.10351 “View on arXiv” Authors: Leonardo Baggiani, Martin Herdegen, Nazem Khan Abstract We revisit the problem of portfolio selection, where an investor maximizes utility subject to a risk constraint. Our framework is very general and accommodates a wide range of utility and risk functionals, including non-concave utilities such as S-shaped utilities from prospect theory and non-convex risk measures such as Value at Risk. Our main contribution is a novel and complete characterization of well-posedness for utility-risk portfolio selection in one period that takes the interplay between the utility and the risk objectives fully into account. We show that under mild regularity conditions the minimal necessary and sufficient condition for well-posedness is given by a very simple either-or criterion: either the utility functional or the risk functional need to satisfy the axiom of sensitivity to large losses. This allows to easily describe well-posedness or ill-posedness for many utility-risk pairs, which we illustrate by a large number of examples. In the special case of expected utility maximization without a risk constraint (but including non-concave utilities), we show that well-posedness is fully characterised by the asymptotic loss-gain ratio, a simple and interpretable quantity that describes the investor’s asymptotic relative weighting of large losses versus large gains. ...

Ultrafast Extreme Events: Empirical Analysis of Mechanisms and Recovery in a Historical Perspective ArXiv ID: 2509.10376 “View on arXiv” Authors: Luca Henrichs, Anton J. Heckens, Thomas Guhr Abstract To understand the emergence of Ultrafast Extreme Events (UEEs), the influence of algorithmic trading or high-frequency traders is of major interest as they make it extremely difficult to intervene and to stabilize financial markets. In an empirical analysis, we compare various characteristics of UEEs over different years for the US stock market to assess the possible non-stationarity of the effects. We show that liquidity plays a dominant role in the emergence of UEEs and find a general pattern in their dynamics. We also empirically investigate the after-effects in view of the recovery rate. We find common patterns for different years. We explain changes in the recovery rate by varying market sentiments for the different years. ...

Bitcoin Price Forecasting Based on Hybrid Variational Mode Decomposition and Long Short Term Memory Network ArXiv ID: 2510.15900 “View on arXiv” Authors: Emmanuel Boadi Abstract This study proposes a hybrid deep learning model for forecasting the price of Bitcoin, as the digital currency is known to exhibit frequent fluctuations. The models used are the Variational Mode Decomposition (VMD) and the Long Short-Term Memory (LSTM) network. First, VMD is used to decompose the original Bitcoin price series into Intrinsic Mode Functions (IMFs). Each IMF is then modeled using an LSTM network to capture temporal patterns more effectively. The individual forecasts from the IMFs are aggregated to produce the final prediction of the original Bitcoin Price Series. To determine the prediction power of the proposed hybrid model, a comparative analysis was conducted against the standard LSTM. The results confirmed that the hybrid VMD+LSTM model outperforms the standard LSTM across all the evaluation metrics, including RMSE, MAE and R2 and also provides a reliable 30-day forecast. ...

Causal PDE-Control for Adaptive Portfolio Optimization under Partial Information ArXiv ID: 2509.09585 “View on arXiv” Authors: Alejandro Rodriguez Dominguez Abstract Classical portfolio models tend to degrade under structural breaks, whereas flexible machine-learning allocators often lack arbitrage consistency and interpretability. We propose Causal PDE-Control Models (CPCMs), a framework that links structural causal drivers, nonlinear filtering, and forward-backward PDE control to produce robust, transparent allocation rules under partial information. The main contributions are: (i) construction of scenario-conditional risk-neutral measures on the observable filtration via filtering, with an associated martingale representation; (ii) a projection-divergence duality that quantifies stability costs when deviating from the causal driver span; (iii) a causal completeness condition showing when a finite driver span captures systematic premia; and (iv) conformal transport and smooth subspace evolution guaranteeing time-consistent projections on a moving driver manifold. Markowitz, CAPM/APT, and Black-Litterman arise as limit or constrained cases; reinforcement learning and deep hedging appear as unconstrained approximations once embedded in the same pricing-control geometry. On a U.S. equity panel with 300+ candidate drivers, CPCM solvers achieve higher performance, lower turnover, and more persistent premia than econometric and ML benchmarks, offering a rigorous and interpretable basis for dynamic asset allocation in nonstationary markets. ...

DeepAries: Adaptive Rebalancing Interval Selection for Enhanced Portfolio Selection ArXiv ID: 2510.14985 “View on arXiv” Authors: Jinkyu Kim, Hyunjung Yi, Mogan Gim, Donghee Choi, Jaewoo Kang Abstract We propose DeepAries , a novel deep reinforcement learning framework for dynamic portfolio management that jointly optimizes the timing and allocation of rebalancing decisions. Unlike prior reinforcement learning methods that employ fixed rebalancing intervals regardless of market conditions, DeepAries adaptively selects optimal rebalancing intervals along with portfolio weights to reduce unnecessary transaction costs and maximize risk-adjusted returns. Our framework integrates a Transformer-based state encoder, which effectively captures complex long-term market dependencies, with Proximal Policy Optimization (PPO) to generate simultaneous discrete (rebalancing intervals) and continuous (asset allocations) actions. Extensive experiments on multiple real-world financial markets demonstrate that DeepAries significantly outperforms traditional fixed-frequency and full-rebalancing strategies in terms of risk-adjusted returns, transaction costs, and drawdowns. Additionally, we provide a live demo of DeepAries at https://deep-aries.github.io/, along with the source code and dataset at https://github.com/dmis-lab/DeepAries, illustrating DeepAries’ capability to produce interpretable rebalancing and allocation decisions aligned with shifting market regimes. Overall, DeepAries introduces an innovative paradigm for adaptive and practical portfolio management by integrating both timing and allocation into a unified decision-making process. ...

Note on pre-taxation reported data by UK FTSE-listed companies. A search for Benford’s laws compatibility ArXiv ID: 2509.09415 “View on arXiv” Authors: Marcel Ausloos, Probowo Erawan Sastroredjo, Polina Khrennikova Abstract Pre-taxation analysis plays a crucial role in ensuring the fairness of public revenue collection. It can also serve as a tool to reduce the risk of tax avoidance, one of the UK government’s concerns. Our report utilises pre-tax income ($PI$) and total assets ($TA$) data from 567 companies listed on the FTSE All-Share index, gathered from the Refinitiv EIKON database, covering 14 years, i.e., the period from 2009 to 2022. We also derive the $PI/TA$ ratio, and distinguish between positive and negative $PI$ cases. We test the conformity of such data to Benford’s Laws,- specifically studying the first significant digit ($Fd$), the second significant digit ($Sd$), and the first and second significant digits ($FSd$). We use and justify two pertinent tests, the $χ^2$ and the Mean Absolute Deviation (MAD). We find that both tests are not leading to conclusions in complete agreement with each other, - in particular the MAD test entirely rejects the Benford’s Laws conformity of the reported financial data. From the mere accounting point of view, we conclude that the findings not only cast some doubt on the reported financial data, but also suggest that many more investigations be envisaged on closely related matters. On the other hand, the study of a ratio, like $PI/TA$, of variables which are (or not) Benford’s Laws compliant add to the literature debating whether such indirect variables should (or not) be Benford’s Laws compliant. ...

Optimal Investment and Consumption in a Stochastic Factor Model ArXiv ID: 2509.09452 “View on arXiv” Authors: Florian Gutekunst, Martin Herdegen, David Hobson Abstract In this article, we study optimal investment and consumption in an incomplete stochastic factor model for a power utility investor on the infinite horizon. When the state space of the stochastic factor is finite, we give a complete characterisation of the well-posedness of the problem, and provide an efficient numerical algorithm for computing the value function. When the state space is a (possibly infinite) open interval and the stochastic factor is represented by an Itô diffusion, we develop a general theory of sub- and supersolutions for second-order ordinary differential equations on open domains without boundary values to prove existence of the solution to the Hamilton-Jacobi-Bellman (HJB) equation along with explicit bounds for the solution. By characterising the asymptotic behaviour of the solution, we are also able to provide rigorous verification arguments for various models, including – for the first time – the Heston model. Finally, we link the discrete and continuous setting and show that that the value function in the diffusion setting can be approximated very efficiently through a fast discretisation scheme. ...

Community-level Contagion among Diverse Financial Assets ArXiv ID: 2509.15232 “View on arXiv” Authors: An Pham Ngoc Nguyen, Marija Bezbradica, Martin Crane Abstract As global financial markets become increasingly interconnected, financial contagion has developed into a major influencer of asset price dynamics. Motivated by this context, our study explores financial contagion both within and between asset communities. We contribute to the literature by examining the contagion phenomenon at the community level rather than among individual assets. Our experiments rely on high-frequency data comprising cryptocurrencies, stocks and US ETFs over the 4-year period from April 2019 to May 2023. Using the Louvain community detection algorithm, Vector Autoregression contagion detection model and Tracy-Widom random matrix theory for noise removal from financial assets, we present three main findings. Firstly, while the magnitude of contagion remains relatively stable over time, contagion density (the percentage of asset pairs exhibiting contagion within a financial system) increases. This suggests that market uncertainty is better characterized by the transmission of shocks more broadly than by the strength of any single spillover. Secondly, there is no significant difference between intra- and inter-community contagion, indicating that contagion is a system-wide phenomenon rather than being confined to specific asset groups. Lastly, certain communities themselves, especially those dominated by Information Technology assets, tend to act as major contagion transmitters in the financial network over the examined period, spreading shocks with high densities to many other communities. Our findings suggest that traditional risk management strategies such as portfolio diversification through investing in low-correlated assets or different types of investment vehicle might be insufficient due to widespread contagion. ...