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.
Highlights
IntroductionA common measure to assess risks that an insurer is exposed to is the so-called ruin probability
With the ever growing popularity of bonus-malus systems in the car insurance industry, one interesting question to study is whether it really reduces the associated risk and by how much.A common measure to assess risks that an insurer is exposed to is the so-called ruin probability.Motivated by such questions, we derive ruin probabilities in models with a dependence structure that captures the key feature of a simple bonus system, namely that there is a premium discount when no claims are observed in the previous year
We derive ruin probabilities in models with a dependence structure that captures the key feature of a simple bonus system, namely that there is a premium discount when no claims are observed in the previous year
Summary
A common measure to assess risks that an insurer is exposed to is the so-called ruin probability Motivated by such questions, we derive ruin probabilities in models with a dependence structure that captures the key feature of a simple bonus system, namely that there is a premium discount when no claims are observed in the previous year. We derive ruin probabilities in models with a dependence structure that captures the key feature of a simple bonus system, namely that there is a premium discount when no claims are observed in the previous year Inspired by this feature, we found a regenerative structure within inter-claim times that could describe the properties of an analogous bonus system, referred to as a no claims discount (NCD) system. In reality, one could find violations of such an assumption
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