无单调性条件且Lévy测度无穷的带相互连接障碍的积分-偏微分方程组的粘性解
Viscosity solution of systems of integral-partial differential equations with interconnected obstacles without Monotonicity Conditions and infinite L{é}vy measure
- Le Mans Université（勒芒大学）
- University of Tunis El Manar（突尼斯艾曼大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文在无单调性条件且Lévy测度无穷的设定下，通过反射倒向随机微分方程工具，构造了带相互连接障碍的积分-偏微分方程组的连续粘性解并证明其唯一性。
中文摘要 AI 辅助
本文研究了一类带相互连接障碍的二阶积分-偏微分方程组。一个特殊情形是与跳跃扩散模型中最优切换问题相关的Hamilton-Jacobi-Bellman（简称HJB）方程组。通过去掉生成元关于跳跃分量的单调性条件，我们构造了该方程组的一个连续粘性解，该解在连续有界函数类中是唯一的。Lévy测度$\lambda(.)$具有无穷活动性。我们使用的主要工具是带跳跃和相互连接障碍的反射倒向随机微分方程的相应方程组，我们也研究了该方程组解的存在唯一性。
英文摘要
In this paper, we study a system of second-order integral-partial differential equations with interconnected obstacles. A particular case, is the Hamilton-Jacobi-Bellman (HJB for short) system associated with the optimal switching problem in the jump-diffusion model. Getting rid of the monotonicity condition on the generators with respect to the jump component, we construct a continuous viscosity solution of the system, which is unique in the class of continuous bounded functions. The L{é}vy measure $λ$(.) is of infinite activity. The main tool we use is the associated system of reflected backward stochastic differential equations with jumps and interconnected obstacles for which we also study existence and uniqueness of the solution.
