时间：2019年11月20日(周三) 下午13：30-14：30
地点：中北校区理科大楼A1716报告厅
题目：Optimal investment and reinsurance to minimize the probability of drawdown with borrowing costs
报告人：梁志彬 南京师范大学数学科学学院 教授
摘要：
We study the optimal investment and reinsurance problem in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component and the borrowing rate is higher than the lending rate. The objective is to minimize the probability of drawdown, namely, the probability that the value of the wealth process reaches some fixed proportion of its maximum value to date. By the method of stochastic control theory and the corresponding Hamilton-Jacobi-Bellman equation, we investigate the optimization problem in two different cases and divide the whole region into four subregions. The explicit expressions of the optimal investment/reinsurance strategies and the minimum probability of drawdown are derived. We find that when wealth is at a relatively low level (below the borrowing level), it is optimal to borrow money to invest in the risky asset; when wealth is at a relatively high level (above the saving level), it is optimal to save more money; while between them, the insurer is willing to invest all the wealth in the risky asset. In the end, some comparisons are presented to show the impact of higher borrowing rate on the optimal results.
报告人简介：
梁志彬，女，博士，南京师范大学数学科学学院教授，博士生导师。主要研究方向：风险管理与精算，数理金融与定价，随机最优风险控制。08 年以来，应邀访问过英国London Imperial College 的Tanaka 商学院；美国University of Michigan 的数学系（先后三年半）；加拿大Concordia University 的数学与统计系；美国北卡州立大学数学系；以及多次访问香港大学的统计与精算系。自2007 年以来，一直担任美国《数学评论》评论员；同时，担任国家自然科学基金委员会数理科学部的通讯评议专家，以及教育部学位中心网上通讯评议专家。