AI 中文总结
研究由非齐次简单列维过程驱动的双重反射倒向随机微分方程，用惩罚方法建立存在唯一性结果与比较原理，给出美式博弈期权估值和广义 Dynkin 博弈等应用，并在合适假设下建立博弈鞍点存在性。
AI 中文摘要
我们研究了在非齐次列维过程生成的滤波中具有跳跃以及两个完全分离的左极限右连续障碍的双重反射倒向随机微分方程。通过惩罚方法在驱动项的随机利普希茨条件下建立了存在性和唯一性结果。我们还证明了比较原理并给出了两个密切相关的应用。第一个涉及此类列维市场中美式博弈期权的非线性估值，第二个解决了非线性期望下的相关广义 Dynkin 博弈。此外，在障碍的适当半连续性假设下，我们建立了博弈的鞍点存在性。
英文摘要
We study doubly reflected backward stochastic differential equations with jumps and two completely separated right-continuous with left limits barriers in a filtration generated by an inhomogeneous Levy process. We establish existence and uniqueness results under a stochastic Lipschitz condition on the driver by means of a penalization method. We also prove a comparison principle and present two closely related applications. The first concerns the nonlinear valuation of an American game option in such a Levy market, while the second addresses the associated generalized Dynkin game under nonlinear expectation. Moreover, under suitable semicontinuity assumptions on the barriers, we establish the existence of a saddle point for the game.
