Quality & Quantity

, Volume 47, Issue 2, pp 791–802

# Fractional mortality rate based on rational interpolating method and its application in actuarial science

Article

## Abstract

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.

## Keywords

Rational interpolating method Fractional death assumption Mortality rate Actuarial present value

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## References

1. 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
2. Duan Q., Djidjeli K., Price W.G., Twizell E.H.: Rational cubic spline based on function values. Comp. Graph. 22(4), 479–486 (1998)
3. 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
4. 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
5. Frostig E.: Properties of the power family of fractional age approximations. Insur. Math. Econ. 33, 163–171 (2003)
6. Gerber H.U.: Life Insurance Mathematics. Springer-verlag, Berlin (1997)Google Scholar
7. Jones B.L., Mereu J.A.: A family of fractional age assumptions. Insur. Math. Econ. 27, 261–276 (2000)
8. Jones B.L., Mereu J.A.: A critique of fractional age assumptions. Insur. Math. Econ. 30, 363–370 (2002)
9. Li X., Zeng Q.: Actuarial Mathematics in Life Insurance. Nankai University Press, Tannin (2001)Google Scholar
10. Schmidt J.W., Hess W.: Positivity of cubic polynomials on intervals and positive spline interpolation. BIT Num. Math. 28(2), 340–352 (1988)