Ruin probability in a correlated aggregate claims model with common Poisson shocks: application to reinsurance.

*(English)*Zbl 1349.91141Summary: This paper considers a correlated aggregate claims model with common Poisson shocks, which allows for dependence in \(n\) (\(n \geq 2\)) classes of business across \(m\) (\(m \geq 1\)) different types of stochastic events. The dependence structure between different claim numbers is connected with the thinning procedure. Under combination of quota-share and excess of loss reinsurance arrangements, we examine the properties of the proposed risk model. An upper bound for the ruin probability determined by the adjustment coefficient is established through martingale approach. We reduce the problem of optimal reinsurance strategy for maximizing the insurer’s adjustment coefficient and illustrate the results by numerical examples.

Reviewer: Reviewer (Berlin)

##### MSC:

91B30 | Risk theory, insurance (MSC2010) |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

##### Keywords:

common Poisson shocks; thinning procedure; ruin probability; adjustment coefficient; optimal reinsurance
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\textit{X. Hu} and \textit{L. Zhang}, Methodol. Comput. Appl. Probab. 18, No. 3, 675--689 (2016; Zbl 1349.91141)

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