Frontiers of Mathematics in China >

2015 , Vol. 10 >Issue 6: 1433 - 1447

DOI: 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 LIU 3
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  • 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

Received date: 06 May 2015

Accepted date: 24 Jun 2015

Published date: 12 Oct 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Sparre Andersen risk model; Erlang inter-claim times; ruin probability; Lundberg bound; Cramér-Lundberg approximation

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]. Frontiers of Mathematics in China, 2015 , 10(6) : 1433 -1447 . DOI: 10.1007/s11464-015-0492-9

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