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

References

[1] Lu F X. Zeng Q W. Life Insurance Actuarial Mathematics. Tianjin: Press of Nankai University, 2001

[2] Hu G. Life Insurance Mathematics. Berlin: Springer-Verlag, 1997

[3] Jia N N. Hu Y Q. The crisis analysis and management based on the variable interest rate of Chinese life insurance company. In: Proceedings of the Second China Workshop on Information System of Crisis Response and Management. Harbin, China: Harbin Engineering University Press, 2007, 277-281

[4] Beekman J A, Fuelling C P. Interest and mortality randomness in some annuities. Insurance, Mathematics and Economics, 1990, 9(2-3): 185-196

[5] Beekman J A, Fuelling C P. Extra randomness in certain annuity models. Insurance, Mathematics & Economics, 1992, 10(4): 275-287

[6] Norberg R. A solvency study in life insurance. In: Proceedings of the third AFIR International Colloquium. Rome. 1993: 822-830

[7] Parker G. Moments of the present value of a portfolio of policies. Scandinavian Actuarial Journal, 1994, 77(1): 53-67

[8] Parker G. Limiting distribution of the present value of a portfolio. Astin Bulletin, 1994, 24(1): 47-60

[9] Norberg R. Acontinuous-time Markov chain interest model with applications to insurance. Journal of Applied Stochastic Models and Data Analysis, 1995(11): 245-256

[10] Norberg R. Bonus in life insurance: principles and prognoses in a stochastic environment. Insurance: Mathematice and Economics, 1997, 20(2): 145

[11] Norberg R. Discussion in: Parker G. (1997), Stochastic analysis of the interaction between investment and insurance risks. North American Actuarial Journal, 1997b

[12] Liu L Y, Liu R M. A class of increasing payment life insurance under the stochastic interest. Operations Research and Management Science, 2005, 14(2): 125-128

[13] Wang L Y, Liu Y. Reserves and analysis of the risk in life insurance with interest randomness. Journal of Dalian University, 2003, 24(4): 17-20

Acknowledgement

This work was supported in part by the Science and Technology Research Project of Heilongjiang Education Department (11544021)

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg