A class of life insurance reserve model and risk analysis in a stochastic interest rate environment

Abstract

Actuarial theory in a stochastic interest rate environment is an active research area in life insurance; business and life insurance reserves are one of the key contents in actuarial theory. In this study, an interest force accumulation function model with a Gauss process and a Poisson process is proposed as the basis for the reserve model. With the proposed model, the net premium reserve model, which is based on the semi-continuous variable payment life insurance policy, is approximated. Based on this reserve model, the future loss variance model is proposed and the risk, which is caused by drawing on the reserve, is analyzed and evaluated. Subsequently, assuming a uniform distribution of death (UDD) the reserve and future loss variance models are also provided. Finally, a numerical example is presented for illustration and verification purposes. Using the numerical calculation, the relationships between reserve, future loss variance and model parameters are analyzed. The conclusions are a good fit to real life insurance practices.

Keywords

reserve / loss variance / stochastic interest rate

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Higher Education Press and Springer-Verlag Berlin Heidelberg