论文标题
随机最大原理默认
Stochastic Maximum Principle with Default
论文作者
论文摘要
在本文中，我们得出了随机最佳控制问题的足够和必要的最大原理，其中系统状态由受控的随机微分方程（默认值）给出。我们证明存在对受控默认随机微分方程的独特解决方案。此外，我们证明了解决与最大原理有关的后向后随机微分方程的解决方案的存在和唯一性。最后，我们将最大原则应用于对数实用程序函数解决实用性最大化问题。
In this paper, we derive sufficient and necessary maximum principles for a stochastic optimal control problem where the system state is given by a controlled stochastic differential equation with default. We prove existence of a unique solution to the controlled default stochastic differential equation. Furthermore, we prove existence and uniqueness of solution to the adjoint backward stochastic differential equation which appears in connection to the maximum principles. Finally, we apply the maximum principles to solve a utility maximisation problem with logarithmic utility functions.
