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中国管理科学

中国管理科学 ›› 2009, Vol. 17 ›› Issue (4): 46-52.

• 论文 • 上一篇    下一篇

最大化生存概率的投资策略

罗琰1,2, 杨招军1, 杨金强1   

  1. 1. 湖南大学经济与贸易学院, 湖南长沙410079;
    2. 南京审计学院数学与统计学院, 江苏南京210075
  • 收稿日期:2008-09-08 修回日期:2009-07-08 出版日期:2009-08-30 发布日期:2009-08-30
  • 作者简介:罗琰(1979- ),男(汉族),湖南郴州人,湖南大学经济与贸易学院博士研究生,南京审计学院数学与统计学院讲师,研究方向:金融数学、金融工程.
  • 基金资助:

    国家社科基金资助项目(06BJL022);湖南大学“985工程”哲学社会科学创新基地项目

Optimal Investment for Maximizing the Survival Probability

LUO Yan1,2, YANG Zhao-jun1, YANG Jin-qiang1   

  1. 1. School of Economics and Trade, Hunan University, Changsha 410079, China;
    2. School of Mathematics and Statistics, Nanjing University of Audit, Nanjing 210075, China
  • Received:2008-09-08 Revised:2009-07-08 Online:2009-08-30 Published:2009-08-30

PDF (PC)

1509

被引次数

19

摘要： 本文研究最大化生存概率准则下的最优投资问题。假设投资者面临着不可对冲的随机风险,市场是不完备的,任何投资策略都不能完全消除财富总量的下行风险。本文主要结果是:假设无风险资产利率大于零,分别研究了无借贷约束和有借贷约束条件下基于最大化生存概率准则的最优投资问题,运用随机控制理论,通过求解HJB方程,获得了最优投资策略及相应最大生存概率的闭式解,给出了数值算例,通过比较静态分析揭示了生存概率和投资策略与各参数之间的数量关系。结果表明,风险资产最优投资比例随财富总量的增加而减少,企业的生存概率随财富总量的增加而增加,随法定水平的增加而减少。

关键词: 生存概率, 随机控制, 借贷约束, 下行风险

Abstract: In this paper, we study the problem of optimal investment based on the criteria of maximizing probability of survival. On the assumption that investor is faced with a random risk process, the market is incomplete, and the risk of going down-side to the investor cannot be completely eliminated no matter what the investment strategy is. The main contributions are summed up as follows: Based on the maximizing probability of survival, we consider the optimal problem with and without the restriction of borrowing respectively if the risk-free is greater than zero. The closed-form expressions of the optimal strategy and the optimal value function are derived via solving the corresponding HJB equation. In addition, the compares tive static analysis is presented, which explains the quantitative relations among the parameters, survival probability and investment strategy. The results indicate that the proportion invested in the risk asset decreases as the wealth level increases. The more the amount of wealth or the less the given goal level, the greater the survival probability.

Key words: survival probability, stochastic control, borrowing constraints, downside risk

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