Stochastic Control Problems with State Reflections Based on Relaxed Benchmark Tracking
时间  Datetime
2025-12-04 14:00 — 15:00
地点  Venue
腾讯会议APP2()
报告人  Speaker
薄立军
单位  Affiliation
西安电子科技大学
邀请人  Host

腾讯会议号: 184 893 614 会议密码: 460732
报告摘要  Abstract

This talk discusses the Merton's optimal portfolio and consumption problem in an extended

formulation by incorporating the benchmark tracking on the wealth process. We consider a

tracking formulation such that the wealth process compensated by a fictitious capital injection

outperforms the benchmark at all times. The fund manager aims to maximize the expected

utility of consumption deducted by the cost of the capital injection, where the latter term

can also be interpreted as the expected largest shortfall of the wealth with reference to the

benchmark. By considering an auxiliary state process, we formulate an equivalent stochastic

control problem with state reflections at zero. For general utility functions and Ito's diffusion

benchmark process, we develop a convex duality theorem, new to the literature, to the auxiliary stochastic control problem with state reflections in which the dual process also exhibits

reflections from above. For CRRA utility and geometric Brownian motion benchmark process, we further derive the optimal portfolio and consumption in feedback form using the new

duality theorem, allowing us to discuss some interesting financial implications induced by the

additional risk-taking from the capital injection and the goal of tracking.
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