报告人：尹居良教授 广州大学

时间：2023年11月30日上午10:00

地点：数学与信息学院数学系605

报告摘要：This talk is concerned with the optimal investment and risk control problem for an insurer subject to a stochastic economic factor in a Lévy market. In our mathematical model, a riskless bond and a risky asset are assumed to rely on a stochastic economic factor which is described by a Lévy stochastic differential equation (SDE). The risk process is described by a new “jump diffusion” SDE depending on the stochastic economic factor and is negatively correlated with capital gains in the financial market. Using expected utility maximization, we characterize the optimal strategies of investment and risk control under the logarithmic utility function and the power utility function, respectively. With the logarithmic utility assumption, we use the classical optimization method to obtain the optimal strategy. However, for the power utility function, we apply dynamic programming principle to derive the Hamilton–Jacobi–Bellman (HJB) equation, and analyze its solution in order to obtain the optimal strategy. We also show the verification theorem. Finally, to study the impact of the market parameters on the optimal strategies, we conduct a numerical analysis.
报告人简介：尹居良，2003年博士毕业于中山大学概率论与数理统计专业。现为广东省珠江学者特聘教授，广州大学“广州学者”特聘教授，统计学专业博士生导师，经济与统计学院副院长。担任中国现场统计研究会常务理事、广东省高校统计学教学指导委员会副主任和中国工业与应用数学学会系统与控制数学专业委员会委员等职务。主要从事随机分析与随机控制、数理金融与保险精算、时间序列分析等领域的教学与研究工作。先后主持承担省部级科研项目7项、国家自然科学基金项目3项，正式发表各类学术论文60余篇，其中被SCI和SSCI索引收录40篇，有2篇入选ESI高被引论文。2007年和2008年分别获广东省统计科学研究成果一等奖和全国优秀统计成果三等奖。

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