Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2013; 50(2): 611-626

Printed March 31, 2013

https://doi.org/10.4134/BKMS.2013.50.2.611

Copyright © The Korean Mathematical Society.

Uniform asymptotics for the finite-time ruin probability in a general risk model with pairwise quasi-asymptotically independent claims and constant interest force

Qingwu Gao and Yang Yang

Nanjing Audit University, Nanjing Audit University

Abstract

In the paper we study the finite-time ruin probability in a general risk model with constant interest force, in which the claim sizes are pairwise quasi-asymptotically independent and arrive according to an arbitrary counting process, and the premium process is a general stochastic process. For the case that the claim-size distribution belongs to the consistent variation class, we obtain an asymptotic formula for the finite-time ruin probability, which holds uniformly for all time horizons varying in a relevant infinite interval. The obtained result also includes an asymptotic formula for the infinite-time ruin probability.

Keywords: uniform asymptotics, finite-time ruin probability, pairwise quasi-asymptotic independence, consistent variation

MSC numbers: 62P05, 62E20, 60F05