报 告 人：薄立军教授（中国科学技术大学）

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

报告时间：2018年3月30日15:00-16:00

报告地点：知新楼B座1238

报告摘要：

We study an openproblem of risk-sensitive portfolio allocation in a regime-switching creditmarket with default contagion. The state space of the Markovianregime-switching process is assumed to be a countably infinite set. Tocharacterize the value function of the risk sensitive stochastic controlproblem, we investigate the corresponding recursive infinite-dimensionalnonlinear dynamical programming equations (DPEs) based on default states. Wepropose to work in the following procedure: Applying the theory of the monotonedynamical system, we first establish the existence and uniqueness of classicalsolutions to the recursive DPEs by a truncation argument in the finite statespace. Moreover, the associated optimal feedback strategy is characterized bydeveloping a rigorous verification theorem. Building upon results in the firststage, we construct a sequence of approximating risk sensitive control problemswith finite state space and prove that the resulting smooth value functionswill converge to the classical solution of the original system of DPEs. Theconstruction and approximation of the optimal feedback strategy for theoriginal problem are thoroughly discussed.

被告人简历：

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。

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