主 講 人：余翔，香港理工大學應用數(shù)學系副教授
報告時間：2025年4月17日上午10：00—11：00
報告地點：覽秀樓105學術報告廳
報告摘要: This paper studies a Merton's optimal portfolio and consumption problem in an extended formulation by incorporating the benchmark tracking on the wealth process. We consider a relaxed 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 regarded 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 benchmark process, we rigorously develop a convex duality theorem, new to the literature, to the stochastic control problem with state reflections in which our dual process also exhibits reflections from above at a constant barrier. For power utility and geometric Brownian motion benchmark process, we can 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.
主講人簡介： 余翔，香港理工大學應用數(shù)學系副教授。2007 年在華中科技大學獲得數(shù)學學士學位，2012 年在德克薩斯大學奧斯汀分校獲得數(shù)學博士學位。研究方向包括數(shù)學金融、應用概率與隨機分析、隨機控制與優(yōu)化。他最近的研究重點是一些路徑依賴的最優(yōu)投資和消費問題、兩層平均場博弈、時間不一致的最優(yōu)停止問題、新風險模型中的最優(yōu)分紅、具有學習方法的隨機控制和最優(yōu)停止等。相關成果發(fā)表在 《Mathematical Finance》, 《Finance and Stochastics》, 《Annals of Applied Probability》, 《Mathematics of Operations Research》, 《SIAM Journal on Control and Optimization》等期刊上。
