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arXiv · 1706.08880

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

Brahim El Asri·Sehail Mazid
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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.

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Brahim El Asri, Sehail Mazid. 2017-06-25. Zero-sum stochastic differential game in finite horizon involving impulse controls. https://doi.org/10.1007/s00245-018-9529-2

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