Ruin Probabilities with Dependence on the Number of Claims within a Fixed Time Window

Corina Constantinescu, Suhang Dai, Weihong Ni and Zbigniew Palmowski
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Corina Constantinescu: Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
Suhang Dai: Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
Weihong Ni: Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
Zbigniew Palmowski: Mathematical Institute, University of Wrocław, Wroclaw 50-384, Poland

Risks, 2016, vol. 4, issue 2, 1-23

Abstract: We analyse the ruin probabilities for a renewal insurance risk process with inter-arrival times depending on the claims that arrive within a fixed (past) time window. This dependence could be explained through a regenerative structure. The main inspiration of the model comes from the bonus-malus (BM) feature of pricing car insurance. We discuss first the asymptotic results of ruin probabilities for different regimes of claim distributions. For numerical results, we recognise an embedded Markov additive process, and via an appropriate change of measure, ruin probabilities could be computed to a closed-form formulae. Additionally, we employ the importance sampling simulations to derive ruin probabilities, which further permit an in-depth analysis of a few concrete cases.

Keywords: regenerative risk process; ruin probability; subexponential distribution; Cramér asymptotics; importance sampling; crude Monte Carlo; Markov additive process (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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