Ruin probability in Sparre Andersen risk model with claim inter-arrival times distributed as Erlang

doi:10.1007/s11464-015-0492-9

Front. Math. China

2015, Vol. 10

Issue (6) : 1433-1447 https://doi.org/10.1007/s11464-015-0492-9

RESEARCH ARTICLE

Ruin probability in Sparre Andersen risk model with claim inter-arrival times distributed as Erlang

Guangkun SUN^1,^*(

),Shuaiqi ZHANG^2,^*(

),Guoxin LIU³

1. School of Science, Hebei University of Technology, Tianjin 300401, China
2. School of Economics and Commerce, Guangdong University of Technology, Guangzhou 510520, China
3. Department of Mathematics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

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Abstract

This article deals with the ruin probability in a Sparre Andersen risk process with the inter-claim times being Erlang distributed in the framework of piecewise deterministic Markov process (PDMP). We construct an exponential martingale by virtue of the extended generator of the PDMP to change the measure. Some results are derived for the ruin probabilities, such as the general expressions for ruin probability, Lundberg bounds, Cramér-Lundberg approximations, and finite-horizon ruin probability.

Keywords Sparre Andersen risk model Erlang inter-claim times ruin probability Lundberg bound Cramér-Lundberg approximation

Corresponding Author(s): Guangkun SUN,Shuaiqi ZHANG

Issue Date: 12 October 2015

Cite this article:

Guangkun SUN,Shuaiqi ZHANG,Guoxin LIU. Ruin probability in Sparre Andersen risk model with claim inter-arrival times distributed as Erlang[J]. Front. Math. China, 2015, 10(6): 1433-1447.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0492-9
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I6/1433

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