Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model |
| |
Authors: | Qihe Tang Kam C Yuen |
| |
Institution: | a Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA b Department of Mathematics, Suzhou University, Suzhou 215006, PR China c Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong |
| |
Abstract: | Consider an insurer who is allowed to make risk-free and risky investments. The price process of the investment portfolio is described as a geometric Lévy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of Pareto type, we obtain a simple asymptotic formula which holds uniformly for all time horizons. The same asymptotic formula holds for the finite-time and infinite-time ruin probabilities. Restricting our attention to the so-called constant investment strategy, we show how the insurer adjusts his investment portfolio to maximize the expected terminal wealth subject to a constraint on the ruin probability. |
| |
Keywords: | primary 91B30 secondary 60G51 60K05 91B28 |
本文献已被 ScienceDirect 等数据库收录! |
|