Discrete-time risk model based on zero inflated poisson time series

Abstract

An important goal of actuary is to develop models for company portfolio and insurance products. Risk measurement is one of the essential measures that inform actuaries and risk managers about the degree to which the risk bearing entity. To have precise risk measure, we require an appropriate claim count process. The common claim count processes are usually constructed from the Poisson distribution. However, insurance data have generally excess zeros which causes the overdispersion. This violates the assumption of the Poisson distribution. Therefore, alternative distributions accommodating zero count are explored in literature. The zero inflated Poisson distribution is one of the distributions widely used for zero count data. In this study, we apply the zero inflated Poisson distribution to construct an integer valued time series for claim counts. The model is then applied to construct risk models based on the zero inflated Poisson time series. We derive some properties and the approximation of the value of the ruin probability of the constructed models. In addition, we also perform some calculations of the value of the ruin probability, the value at risk, and the tail value at risk.