The ANZIAM Journal

  • The ANZIAM Journal (2009), 51 : pp 34-48
  • Copyright © Australian Mathematical Society 2010
  • DOI: 10.1017/S144618110900042X (About DOI)
  • Published online: 09 March 2010

Table of Contents - 2009 - Volume 51, Issue 01  

Cambridge Journals Online - CUP Full-Text Page
The ANZIAM Journal (2009), 51:34-48 Cambridge University Press
Copyright © Australian Mathematical Society 2010
doi:10.1017/S144618110900042X

Research Article

RUIN PROBABILITIES UNDER AN OPTIMAL INVESTMENT AND PROPORTIONAL REINSURANCE POLICY IN A JUMP DIFFUSION RISK PROCESS

YIPING QIANa1 and XIANG LINa2 c1

a1 School of Business, Central South University, Yuelu Mountain, Changsha 410083, Hunan, PR China
a2 School of Mathematics, Central South University, No. 22 South Shaoshan Road, Changsha 410075, Hunan, PR China (email: xlin@csu.edu.cn)
Article author query
qian y [Google Scholar]
lin x [Google Scholar]

Abstract

In this paper, we consider an insurance company whose surplus (reserve) is modeled by a jump diffusion risk process. The insurance company can invest part of its surplus in n risky assets and purchase proportional reinsurance for claims. Our main goal is to find an optimal investment and proportional reinsurance policy which minimizes the ruin probability. We apply stochastic control theory to solve this problem. We obtain the closed form expression for the minimal ruin probability, optimal investment and proportional reinsurance policy. We find that the minimal ruin probability satisfies the Lundberg equality. We also investigate the effects of the diffusion volatility parameter, the market price of risk and the correlation coefficient on the minimal ruin probability, optimal investment and proportional reinsurance policy through numerical calculations.

(Received March 03 2009)

(Revised November 05 2009)

2000 Mathematics subject classificationprimary 60G99; secondary 60G65; 91B30

Keywords and phrasesruin probability; proportional reinsurance; optimal investment policy; Lundberg’s equality; Hamilton–Jacobi–Bellman equation

Correspondence:

c1 For correspondence; e-mail: xlin@csu.edu.cn

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