Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching

报告题目:Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching




摘要: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.

薄立军简历:薄立军现为中国科学技术大学数学科学学院教授,2003年本科毕业于西安电子科技大学数学系,2006年和2009年于南开大学概率论与数理统计专业分别获得硕士和博士学位,主要研究方向为随机分析与金融数学。2012年入选教育部新世纪优秀人才支持计划,目前已在国际公认的金融数学、管理和运筹学以及保险精算领域权威期刊Math. Finan., Finan. & Stoch., SIAM J. Finan. Math., SIAM J. Control Optim., Math. Opers. Res., J. Banking Finan., JEDC,IME和Quant. Finan.上发表学术论文20余篇。