摘  要：

We compute the optimal investment strategy for an individual who wishes to minimize her probability of lifetime ruin. The financial market in which she invests consists of two riskless assets. One riskless asset is a money market, and she consumes from that account. The other riskless asset is a bond that earns a higher interest rate than the money market, but buying and selling bonds is subject to proportional transaction costs. We consider three cases: (1) The individual is allowed to borrow from both riskless assets; ruin occurs if total imputed wealth reaches zero. Under the optimal strategy, the individual does not sell short the bond. However, she might wish to borrow from the money market to fund her consumption. Thus, in the next two cases, we seek to limit borrowing from that account. (2) We assume that the individual pays a higher rate to borrow than she earns on the money market. (3) The individual is not allowed to borrow from either asset; ruin occurs if both the money market and bond accounts reach zero wealth. We prove that the borrowing rate in case (2) acts as a parameter connecting the two seemingly unrelated cases (1) and (3).

报告人简介：梁晓青，河北工业大学理学院讲师，2008年本科毕业于中国农业大学理学院应用数学系，2015年博士毕业于南开大学数学科学学院，主要从事随机过程及随机控制理论在金融保险中的应用等方面的研究，曾赴美国密歇根大学，加拿大西蒙菲莎大学访问学习。目前已发表SCI论文十余篇，主持国家自然科学基金和河北省自然科学基金项目各一项。