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Risks 2016, 4(2), 17; doi:10.3390/risks4020017

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

1
Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
2
Mathematical Institute, University of Wrocław, Wroclaw 50-384, Poland
*
Author to whom correspondence should be addressed.
Academic Editor: Montserrat Guillén
Received: 19 April 2016 / Revised: 4 June 2016 / Accepted: 8 June 2016 / Published: 15 June 2016
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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. View Full-Text
Keywords: regenerative risk process; ruin probability; subexponential distribution; Cramér asymptotics; importance sampling; crude Monte Carlo; Markov additive process regenerative risk process; ruin probability; subexponential distribution; Cramér asymptotics; importance sampling; crude Monte Carlo; Markov additive process
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Constantinescu, C.; Dai, S.; Ni, W.; Palmowski, Z. Ruin Probabilities with Dependence on the Number of Claims within a Fixed Time Window. Risks 2016, 4, 17.

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