Journal of East China Normal University(Natural Sc ›› 2007, Vol. 2007 ›› Issue (1): 70-77.

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Upper Bound for Renewal Risk Model with Stochastic Investment Return(English)

XU Lin1,2, WANG Rong-ming1 , YAO Ding-jun1   

  1. 1. Department of Statistics, East China Normal University, Shanghai 200062, China; 2. School of Mathematics and Computer science, Anhui NormalUniversity, Wuhu Anhui 241000, China
  • Received:2006-04-17 Revised:2006-09-20 Online:2007-01-25 Published:2007-01-25
  • Contact: XU Lin

Abstract: Ruin problems in the ordinary renewal risk model with stochastic investment were examined. The asset price process of investment is denoted by $\{e^{R_t},\ t\geqslant 0\}$, where $R_t$ is assumed to be a L\'{e}vy process. By constructing a supermartingale associated with the ruin time of the surplus process with investment, an upper bound for ultimate ruin probability by
martingale approach was presented. The impact of inter-arrival times of claims on ruin probability was considered by numerical method.

Key words: L\'{e}vy process, ruin probability, martingale , ordinary renewal risk model, L\'{e}vy process, ruin probability, martingale

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