Dynamic Programming for Value-at-risk Markov Decision Processes in Continuous Spaces

By Xian Chen, Erick Delage, Weikai Wang

Rating

1860
Battle Count: 57

Relevance

9/10
Highly relevant as it provides a rigorous theoretical foundation for VaR-based optimal execution strategies in continuous spaces, directly addressing a gap in algorithmic trading literature regarding dynamic risk-adjusted strategies.

Implementation Complexity

8/10
High complexity due to the need for numerical integration (quadrature), root-finding algorithms, and handling of continuous state/action spaces. Requires strong background in stochastic control and numerical methods.

Reproducibility

3/5
The paper provides detailed mathematical derivations, algorithmic steps for numerical computation (Gauss-Legendre quadrature, Brent's method), and specific parameter settings for the application. However, no public code repository URL is provided in the text.

Abstract

Value-at-Risk (VaR) is a widely adopted quantile-based risk measure in practice, yet incorporating VaR objectives into Markov decision processes (VaR MDPs) remains a longstanding challenge. Recent work has derived dynamic programming equations for VaR MDPs in finite state and action spaces but left the case of more general spaces unresolved. This paper establishes, for the first time, the validity of these equations in continuous spaces, for both finite- and infinite-horizon settings. Such cases naturally arise in many real-world dynamic decision-making problems. As an application, we study an optimal execution problem with a VaR objective and demonstrate that our framework enables the characterization of optimal dynamic strategies, resolving an open question in the field.

Links

arXiv:2610.24439 ยท Paper rankings

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