主题: Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching
类型: 学术报告
主办方:
报告人: 薄立军教授(中国科学技术大学)
日期: 2018年3月30日15:00-16:00
地点: 知新楼B座1238
内容: We study an open problem of risk-sensitive portfolio allocation in a regime-switching credit market with default contagion. The state space of the Markovian regime-switching process is assumed to be a countably infinite set. To characterize the value function of the risk sensitive stochastic control problem, we investigate the corresponding recursive infinite-dimensional nonlinear dynamical programming equations (DPEs) based on default states. We propose to work in the following procedure: Applying the theory of the monotone dynamical system, we first establish the existence and uniqueness of classical solutions to the recursive DPEs by a truncation argument in the finite state space. Moreover, the associated optimal feedback strategy is characterized by developing a rigorous verification theorem. Building upon results in the first stage, we construct a sequence of approximating risk sensitive control problems with finite state space and prove that the resulting smooth value functions will converge to the classical solution of the original system of DPEs. The construction and approximation of the optimal feedback strategy for the original problem are thoroughly discussed.