# 소수연령 독립 가정에서 탈퇴율의 성질

Lee, Hang-Suck
이항석

• Published : 2008.12.31
• 216 18

#### Abstract

This paper derives conversion formulas from yearly-based absolute rates of decrements to monthly-based rates of decrement due to cause j under FI (fractional age independence) assumption that is a generalization of UDD assumption. Next, it suggests conversion formulas from monthly-based absoluterates of decrements to monthly-based rates of decrement due to cause j under FI assumption. In addition, it calculates conversion formulas from yearly-based rates of decrement due to cause j to the corresponding monthly-based absolute rates of decrements under FI assumption. Some numerical examples are discussed.

#### Keywords

Absolute rates of decrements;rates of decrement due to cause j;FI(fractional age independence) assumption

#### References

1. Shiu, E. S. W. (1987). Multiple-decrements by Riemann-Stieltjes integration, Actuarial Research Clearing House, 1, 1-4
2. Willmot, G. E. (1997). Statistical independence and fractional age assumptions, North American Actuarial Journal, 1, 84-99 https://doi.org/10.1080/10920277.1997.10595597
3. Jones, B. L. and Mereu, J. A. (2002). A critique of fractional age assumptions, Insurance: Mathematics and Economics, 30, 363-370 https://doi.org/10.1016/S0167-6687(02)00104-X
4. Lee, H. (2008). Generalized conversion formulas between multiple decrement models and associated single decrement models, The Korean Journal of Applied Statistics, 21, 739-754 https://doi.org/10.5351/KJAS.2008.21.5.739
5. Daniel, J. W. (1993). Multiple-decrement models and corresponding conditional single-decrement models, Actuarial Research Clearing House, 1, 229-237
6. Jones, B. L. and Mereu, J. A. (2000). A family of fractional age assumptions, Insurance: Mathematics and Economics, 27, 261-276 https://doi.org/10.1016/S0167-6687(00)00052-4
7. Apostol, T. M. (1974). Mathematical Analysis, Addison-Wesley
8. Bowers, N. L., Jones, D. A., Gerber, H. U., Nesbitt, C. J. and Hickman, J. C. (1997). Actuarial Mathematics, Society of Actuaries
9. Carriere, J. F. (1994). Dependent decrement theory, Transactions of Society of Actuaries, 46, 45-74

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