报告题目:Mean-variance investment and risk control strategies for a dynamic contagion process with diffusion
报 告 人:孙中洋教授(曲阜师范大学)
报告时间:2024年12月19日 11:00-12:00
报告地点:理学院(格物楼)402
报告摘要:
This paper explores an investment and risk control issue within a contagious financial market, specifically focusing on a mean-variance (MV) framework for an insurer. The market's risky assets are depicted via a jump-diffusion model, featuring jumps due to a multivariate dynamic contagion process with diffusion (DCPD). The process envelops several popular processes, including the Hawkes process with exponentially decaying intensity, the Cox process with Poisson shot-noise intensity, and the Cox process with CIR intensity. The model distinguishes between externally excited jumps, indicative of exogenous influences, modeled by the Cox process, and internally excited jumps, representing endogenous factors, captured by the Hawkes process. Given an expected terminal wealth, the insurer seeks to minimize the variance of terminal wealth by adjusting the issuance volume of policies and investing the surplus in the financial market. In order to address this MV problem, we employ a suite of mathematical techniques, including the stochastic maximum principle (SMP), backward stochastic differential equations (BSDEs), and linear-quadratic (LQ) control techniques. These methodologies facilitate the derivation of both the efficient strategy and the efficient frontier. The presentation of the results in a semi-closed form is governed by a non-local partial differential equation (PDE).
报告人简介:
孙中洋,曲阜师范大学教授、博士生导师,山东省高等学校优秀青年创新团队负责人。研究方向包括精算数学、数理金融与随机最优控制。主持国家自然科学基金面上项目1项、青年项目1项,以及省部级项目4项。在《SIAM Journal on Control and Optimization》、《Scandinavian Actuarial Journal》、《Applied Mathematics and Optimization》、《Journal of Optimization Theory and Applications》、《ESAIM: Control,Optimisation and Calculus of Variations》等学术期刊上发表论文20余篇。