Zero-sum games with risk-sensitive cost criterion are considered with underlying dynamics being given by controlled stochastic differential equations. Under the assumption of geometric stability on the dynamics, we completely characterize all possible saddle point strategies in the class of stationary Markov controls. In addition, we also establish existence-uniqueness result for the value function of the Hamilton–Jacobi–Isaacs equation.

中文翻译：

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具有风险敏感成本的零和随机微分对策

考虑具有风险敏感成本准则的零和博弈，并通过受控的随机微分方程给出基本动态。在动力学上具有几何稳定性的假设下，我们完全描述了静态马尔可夫控制类中所有可能的鞍点策略。此外，我们还为Hamilton–Jacobi–Isaacs方程的值函数建立了存在唯一性结果。