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

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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.

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Authors and Affiliations

  1. School of Science, Hebei University of Technology, Tianjin, 300401, China

    Guangkun Sun

  2. School of Economics and Commerce, Guangdong University of Technology, Guangzhou, 510520, China

    Shuaiqi Zhang

  3. Department of Mathematics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Guoxin Liu

Authors
  1. Guangkun Sun
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  2. Shuaiqi Zhang
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  3. Guoxin Liu
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Corresponding authors

Correspondence to Guangkun Sun or Shuaiqi Zhang.

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Sun, G., Zhang, S. & Liu, G. Ruin probability in Sparre Andersen risk model with claim inter-arrival times distributed as Erlang. Front. Math. China 10, 1433–1447 (2015). https://doi.org/10.1007/s11464-015-0492-9

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  • DOI: https://doi.org/10.1007/s11464-015-0492-9

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