论文标题
在时间 - 一致的随机最佳控制问题中的开环平衡方法的PDE方法
A PDE approach for open-loop equilibriums in time-inconsistent stochastic optimal control problems
论文作者
论文摘要
本文研究了具有确定性系数的跳跃扩散SDE下的一般时间内的随机控制问题的开环平衡。受到跳跃前向后的随机微分方程的四步思想的启发（fbsdejs，简而言之），我们得出了两个内格 - 派对微分方程的系统（简称IPDES）。然后，我们严格地证明了验证定理，该定理为开环平衡策略提供了足够的条件。作为一般理论的例证，我们讨论了在跳跃模型下的均值变化投资组合选择问题。
This paper studies open-loop equilibriums for a general class of time-inconsistent stochastic control problems under jump-diffusion SDEs with deterministic coefficients. Inspired by the idea of Four-Step-Scheme for forward-backward stochastic differential equations with jumps (FBSDEJs, for short), we derive two systems of integro-partial differential equations (IPDEs, for short). Then, we rigorously prove a verification theorem which provides a sufficient condition for open-loop equilibrium strategies. As an illustration of the general theory, we discuss a mean-variance portfolio selection problem under a jump-diffusion model.
