数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (2): 313-325.doi: 10.1016/S0252-9602(15)60003-0

• 论文 • 上一篇    下一篇

RUIN PROBABILITY IN THE CONTINUOUS-TIME COMPOUND BINOMIAL MODEL WITH INVESTMENT

张帅琪1, 刘国欣2, 孙梅慈3   

  1. 1. School of Economics and Commerce, Guangdong University of Technology, Guangzhou 510520, China School of Science, Hebei University of Technology, Tianjin 300401, China;
    2. Department of Mathematics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
    3. Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050005, China
  • 收稿日期:2012-07-03 修回日期:2014-04-06 出版日期:2015-03-20 发布日期:2015-03-20
  • 基金资助:

    Shuaiqi Zhang is supported by the Nature Science Foundation of Hebei Province (A2014202202 ) and Guoxin Liu is supported by the Nature Science Foundation of China (11471218).

RUIN PROBABILITY IN THE CONTINUOUS-TIME COMPOUND BINOMIAL MODEL WITH INVESTMENT

Shuaiqi ZHANG1, Guoxin LIU2, Meici SUN3   

  1. 1. School of Economics and Commerce, Guangdong University of Technology, Guangzhou 510520, China School of Science, Hebei University of Technology, Tianjin 300401, China;
    2. Department of Mathematics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
    3. Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050005, China
  • Received:2012-07-03 Revised:2014-04-06 Online:2015-03-20 Published:2015-03-20
  • Supported by:

    Shuaiqi Zhang is supported by the Nature Science Foundation of Hebei Province (A2014202202 ) and Guoxin Liu is supported by the Nature Science Foundation of China (11471218).

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摘要：

This article deals with the problem of minimizing ruin probability under opti- mal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended gen- erator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is obtained.

关键词: The continuous-time compound binomial model, investment, ruin probability, Lundberg bounds

Abstract:

This article deals with the problem of minimizing ruin probability under opti- mal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended gen- erator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is obtained.

Key words: The continuous-time compound binomial model, investment, ruin probability, Lundberg bounds

中图分类号: 

  • 91B30
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