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Constantinescu, Corina
Dai, Suhang
Ni, Weihong
Palmowski, Zbigniew
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[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 4 [Year:] 2016 [Issue:] 2 [Pages:] 1-23
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.
regenerative risk process
ruin probability
subexponential distribution
Cramér asymptotics
importance sampling
crude Monte Carlo
Markov additive process
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