Optimal reinsurance under discrete-time risk model with stochastic premiums and dependence based on integer-valued time series

In this paper, we introduce a discrete-time reinsurance risk model with dependent stochastic premiums and claims, where the premium counts are constructed based on a cross-dependence with the lagged claim counts. The temporal dependence among claims of consecutive periods are modeled by the first-order moving average integer-valued time series. The reinsurance strategy implemented in this study is a combination of the quota-share and excess of loss reinsurance. In our study, we derive the model properties, obtain the optimal retention level that maximizes the adjustment coefficient and obtain the ruin probability. Moreover, we perform multiple numerical simulations to study the impacts of the parameters in the risk model to the ruin probability and the retention level.