RISK-SENSITIVE CREDIT PORTFOLIO OPTIMIZATION UNDER PARTIAL INFORMATION AND CONTAGION RISK

• 成果类型: Article
• 署名作者: Bo, Lijun; Liao, Huafu; Yu, Xiang
• 署名单位: Xidian University; National University of Singapore; Hong Kong Polytechnic University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1735
• 发表日期: 2022
• 页码: 2355-2399
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; Optimal investment; MARKET; BSDEs; driven; jumps; MODEL

摘要

This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has countable states and is unobservable. The stochastic control problem is formulated under partial observations of asset prices and sequential default events. By establishing a martingale representation theorem based on incomplete and phasing out filtration, we connect the control problem to a quadratic BSDE with jumps, in which the driver term is nonstandard and carries the conditional filter as an infinite-dimensional parameter. By proposing some truncation techniques and proving uniform a priori estimates, we obtain the existence of a solution to the 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.