Zero-sum stochastic differential game in finite horizon involving impulse controls

Abstract

This paper considers the problem of two-player zero-sum stochastic differential game with both players adopting impulse controls in finite horizon under rather weak assumptions on the cost functions ($c$ and $\chi$ not decreasing in time). We use the dynamic programming principle and viscosity solutions approach to show existence and uniqueness of a solution for the Hamilton-Jacobi-Bellman-Isaacs (HJBI) partial differential equation (PDE) of the game. We prove that the upper and lower value functions coincide.

arXiv comment30pages, stochastic differential game, impulse control, quasi-variational inequality, viscosity solution. arXiv admin note: text overlap with arXiv:1206.1219 by other authors

References in corpus (4)

• Stochastic Differential Games and Viscosity Solutions of Hamilton-Jacobi-Bellman-Isaacs Equations
• Backward SDEs with constrained jumps and quasi-variational inequalities
• A zero-sum stochastic differential game with impulses, precommitment, and unrestricted cost functions
• Deterministic Minimax Impulse Control in Finite Horizon: the Viscosity Solution Approach

Cited by in corpus (2)

• A fixed-point policy-iteration-type algorithm for symmetric nonzero-sum stochastic impulse control games
• Continuous and Impulse Controls Differential Game in Finite Horizon with Nash-Equilibrium and Application