Abstract

In this paper, we study the two-person zero-sum stochastic games for controlled continuous time Markov chains with risk-sensitive finite-horizon cost criterion. The transition and cost rates are possibly unbounded. For the zero-sum risk-sensitive stochastic game, we prove the existence of the value of the game and a Markov saddle-point equilibrium in the class of all history-dependent multi-strategies under the suitable conditions. We achieve our results by studying the corresponding risk-sensitive finite-horizon optimality equations.

中文翻译：

---

具有风险敏感有限范围成本准则的马尔可夫链的连续时间零和博弈

摘要

在本文中，我们研究了具有风险敏感有限范围成本准则的受控连续时间马尔可夫链的两人零和随机博弈。转换率和成本率可能是无限的。对于零和风险敏感的随机博弈，我们在合适的条件下证明了博弈的价值和马尔可夫鞍点均衡在所有历史依赖的多策略类中的存在性。我们通过研究相应的风险敏感有限范围最优方程来实现我们的结果。