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【预告】“应用概率统计”系列讲座(15):Risk-Sensitive Credit Portfolio Optimization under Partial Information and Contagion Risk
时间:2020-11-15

 

:薄立军   中国科学技术大学

报告时间2020年1123 9:30-12:00

地  点:腾讯会议 ID: 368 132 090

 

摘  要:This talk considers a finite time risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. The Markov regime-switching process is assumed to be unobservable, which has countable states that affect default intensities of surviving assets. The stochastic control problem is formulated under partial observations of asset prices and default events. By proving a novel martingale representation theorem based on incomplete and phasing out filtration, we characterize the value function in an equivalent form. This allows us to connect the control problem to a new type of quadratic BSDE with jumps, in which the driver term has non-standard structures and carries the conditional filter as an infinite-dimensional parameter. By proposing some truncation techniques and establishing a uniform a priori estimates, we obtain the existence of a solution to this BSDE using the convergence of solutions associated to some truncated BSDEs. The verification theorem can be concluded with the aid of our BSDE results, which in turn yields the uniqueness of the solution to the BSDE.

 

报告人简介

  薄立军,中国科学技术大学 教授,研究方向为随机分析、随机控制与金融数学。 2012年入选教育部新世纪优秀人才支持计划,先后主持国家自然科学基金面上项目2(数理学部)、中科院前沿科学重点研究计划-青年拔尖科学家项目。目前已在国际公认的概率统计、金融数学、管理和运筹学权威期刊Math. Finan., SIAM J. Finan. Math., SIAM J. Control & Optim, Math. Opers. Res., J. Banking & Finan., Queueing Syst.上发表学术论文40余篇,出版教材两部。目前担任中国概率统计学会会刊《应用概率统计》编委;美国数学科学研究所(AIMS)旗舰期刊《J. Dynamics & GamesAssociate Editor.