时 间：2025年12月15 日（周一）09：00 – 10：00
地 点：普陀校区理科大楼A1714室
报告人：张鑫 东南大学教授
主持人：李丹萍 华东师范大学教授
摘 要：
In this talk, we investigate a stochastic linear-quadratic (SLQ) control problem for a regime-switching jump-diffusion system. Unlike traditional regime-switching diffusion systems that couple a diffusion process with a Markov chain, we incorporate the jumps of the Markov chain into the state equation. This modeling methodology effectively captures potential gains or losses of the system during the regime transitions. It should be noted that the introduction of Markov chain jumps into the state equation leads to increased complexity in the corresponding coupled differential Riccati equations (CDREs), thereby rendering the solvability of the control problem more challenging. Under the assumption that the cost functional is uniformly convex, we establish the unique solvability of the corresponding CDREs. Building upon this foundation, we derive a closed-loop representation for the unique open-loop optimal control. Finally, we apply our theoretical results to the mean-variance portfolio selection problem in financial markets and obtain its efficient frontier.
报告人简介：
张鑫，东南大学数学学院教授、博士生导师，主要从事随机控制及其在金融保险中的应用方面的研究，共主持国家自然科学基金青年基金1项，国家自然科学基金面上项目3项，教育部博士点专项基金(新教师类) 1 项。在SIAM Journal on Control and Optimization、Insurance Mathematics and Economics、Applied Mathematics and Optimization、Quantitative Finance、Journal of Optimization Theory and Applications、Scandinavian Actuarial Journal等国内外期刊上发表论文三十余篇，先后访问澳大利亚麦考瑞大学、英国利物浦大学、澳门大学、香港理工大学、加拿大约克大学，香港大学等。