Fractional mortality rate based on rational interpolating method and its application in actuarial science
- 271 Downloads
This paper attempts to introduce a new method with adjustable parameter for estimating the mortality of fractional age based on rational interpolating theory. The efficiency analysis of the method is given and some conditions the adjustable parameter should satisfy are given in order to meet the need of actuarial practice. We also analyze the relationship between our estimating method and the one based on UDD assumption—the most commonly used in actuarial study and practice. The result shows that the latter is just a special case of our results. Finally we apply our method to the calculations of actuarial present value of life insurance and annuities. Simulations are also done to give a clear comparison between traditional method and our method specified in this paper.
KeywordsRational interpolating method Fractional death assumption Mortality rate Actuarial present value
Unable to display preview. Download preview PDF.
- Bowers N.L., Gerber H.U., Hickman J.C., Jones D.A., Nesbitt C.J.: Actuarial Mathematics, 2nd edn. The Society of Actuaries, Schaumburg (1997)Google Scholar
- Duan Q., Liu A.K., Cheng F.H.: Constrained interpolation using rational cubic spline with linear denominator. Korean J. Comput. Appl. Math. 6(1), 203–215 (1999)Google Scholar
- Duan, Q., Chen,T., Djidjeli, K., Price, W.G., Twizell, E.H.: A method of shape control of curve design. In: Proceedings of Geometric Modeling and Processing. IEEE Computer Society, pp. 184–189 (2000)Google Scholar
- Gerber H.U.: Life Insurance Mathematics. Springer-verlag, Berlin (1997)Google Scholar
- Li X., Zeng Q.: Actuarial Mathematics in Life Insurance. Nankai University Press, Tannin (2001)Google Scholar