报告人：薄立军 教授（西安电子科技大学）

时间：2025年10月16日 14:00-

腾讯会议ID：953 941 490

摘要：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.

邀请人：周国立

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