Heterogeneity and uncertainty in a multistate framework

Abstract

This research develops the scheme proposed in the paper Pollard [J Inst Actuar 96(2): 251–264, 1970], which is based on a two-state model for the analysis of 1-year mortality, but the results are also valid for the probabilities related to other types of insurance events such as disablement and accidents. We extend the Pollard’s original scheme into time-discrete models with more states (active-invalid-dead) together with further investigation into multi-year time horizon. Additionally, hypotheses for real-valued individual frailty are assumed in the models. As the baseline probabilistic structure, we have adopted a traditional three-state model in a Markov context. We focus on an insurance portfolio. Our outputs of interest are based on the probability distributions of the annual payouts for term insurance policies providing lump sum benefits both in case of death and in case of permanent disability. The analysis of the probability distributions allows us to assess the risk profile of the insurance portfolio, and thus to suggest appropriate actions in terms of premiums and capital allocation. In this regards, we adopt the percentile principle.