Zero-sum Stochastic Differential Games of Impulse Control with Random Intervention Costs

2025/05/12 by Magnus Perninge, Perninge, Magnus
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC) #Reinforcement Learning in Robotics #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2505.07666

openalex publication_date 2025/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a finite-horizon, zero-sum game in which both players control a stochastic differential equation by invoking impulses. We derive a control randomization formulation of the game and use the existence of a value for the randomized game to show that the upper and lower value functions of the original game coincide. The main contribution of the present work is that we can allow intervention costs that are functions of the state as well as time, and that we do not need to impose any monotonicity assumptions on the involved coefficients.

Citations

• Probabilistic Representation for Viscosity Solutions to Double-Obstacle Quasi-Variational Inequalities
• Optimal Stopping of BSDEs with Constrained Jumps and Related Double Obstacle PDEs
• Optimal Stopping of BSDEs with Constrained Jumps and Related Zero-Sum Games
• Optimal switching problems with an infinite set of modes: an approach by\n randomization and constrained backward SDEs
• A probabilistic verification theorem for the finite horizon two-player zero-sum optimal switching game in continuous time
• On the Equality of Solutions of Max-Min and Min-Max Systems of Variational Inequalities with Interconnected Bilateral Obstacles
• Optimal stopping for dynamic risk measures with jumps and obstacle\n problems

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• Non-Markovian Impulse Control Under Nonlinear Expectation