最小化破产概率的最优投资  

Optimal investment for minimizing the probability of bankruptcy

作　　者：罗琰[1,2] 杨招军[2] 

机构地区：[1]南京审计学院数学与统计学院,南京210075 [2]湖南大学金融与统计学院,长沙410079

出　　处：《管理科学学报》2011年第5期77-85,96,共10页Journal of Management Sciences in China

基　　金：国家自然科学基金资助项目(70971037);教育部人文社会科学研究一般资助项目(09YJC790151);教育部博士点基金资助项目(20100161110022);南京审计学院青年课题资助项目(NSK2009/C06)

摘　　要：本文研究基于最小化破产概率准则的最优投资问题.不同于Merton问题中消费是内生决策变量,本文假设投资者单位时间内必须消费不少于一个固定数量的财富,因而投资者有可能最终破产.在三类不同存贷约束条件下,通过求解模型相对应的Ham ilton-Jacobi-Bellmen(HJB)方程,都获得了最优投资策略及最优值函数(破产概率)的闭式解.结果表明,最优投资策略为财富的分段线性函数,而存贷约束特别是不允许贷款约束增加了投资者的破产风险.In this paper we study the problem of optimal investment based on the criteria of minimizing probability of bankruptcy. Different from Merton problem which consumption is a decision variable, there is a positive probability of ruin because investor is forced to pay more than a fixed quantity of money per unit time. Under three different saving and borrowing constraints we get closed-form expressions of Lhe optimal strategy and the optimal value function （ruin probability） by solving the corresponding Hamilton-Jacobi-Bellmen （HJB） equa-tion in each case. The results indicate that the optimal strategy is a piecewise linecr function, and Saving-Bor- rowing constraints, especially borrowing constraints, will increase bankruptcy risk to investor.

关 键 词：破产概率 随机控制 存贷约束 Hamilton-Jacobi—Bellmen方程 

分 类 号：F275[经济管理—企业管理] F830.2[经济管理—国民经济]