Integer-valued time series risk model with surrender and investment

Abstract

In this study, we construct the discrete-time risk models based on integer-valued time series models by incorporating the concepts of surrender and investment. The surrender considered in this study is the situation that the policyholder decides to exit the policy before maturity date. In our study, we provide the probabilistic properties of the model. Moreover, we derive approximation of ruin probabilities of the constructed risk model. Finally, we discuss the trends of the ruin probability and the value at risk of the model by numerical simulations.