Asymptotics of random contractions |
| |
Authors: | Enkelejd Hashorva Anthony G Pakes |
| |
Institution: | a Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Bâtiment Extranef, UNIL-Dorigny, 1015 Lausanne, Switzerlandb School of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, W. A., 6009, Australiac Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242-1409, United States |
| |
Abstract: | In this paper we discuss the asymptotic behaviour of random contractions X=RS, where R, with distribution function F, is a positive random variable independent of S∈(0,1). Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of X assuming that F is in the max-domain of attraction of an extreme value distribution and the distribution function of S satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions. |
| |
Keywords: | primary 60F05 secondary 60G70 |
本文献已被 ScienceDirect 等数据库收录! |
|