A review of discrete-time risk models

Abstract. In this paper, we present a review of results for discrete-time risk models, including the compound binomial risk model and some of its extensions. While most theoretical risk models use the concept of time continuity, the practical reality is discrete. For instance, recursive formulas for discretetime models can be obtained without assuming a claim severity distribution and are readily programmable in practice. Hence the models, techniques used, and results reviewed here for discrete-time risk models are of independent scientific interest. Yet, results for discrete-time risk models can give, in addition, a simpler understanding of their continuous-time analogue. For example, these results can serve as approximations or bounds for the corresponding results in continuous-time models. This paper will serve as a detailed reference for the study of discrete-time risk models.