DOI QR코드

DOI QR Code

Generalized Conversion Formulas between Multiple Decrement Models and Associated Single Decrement Models

다중탈퇴모형과 절대탈퇴모형에서 전환 공식의 일반화

Lee, Hang-Suck
이항석

  • Published : 2008.10.31

Abstract

Researches on conversion formulas between multiple decrement models and the associated single decrement models have focused on calculating yearly-based conversion formulas. In practice, actuaries may be more interested in monthly-based conversion formulas. Multiple decrement tables and their associated single decrement tables consist of yearly-based rates of multiple decrements and absolute rates of decrements, respectively. This paper derives conversion formulas from yearly-based absolute rates of decrements to monthly-based rates of decrement due to cause j under the uniform distribution of decrements(UDD). Next, it suggests conversion formulas from monthly-based absolute rates of decrements to monthly-based rates of decrement due to cause j under UDD. In addition, it calculates conversion formulas from yearly-based rates of decrement due to cause j to the corresponding absolute rates of decrements under UDD or constant force assumption. Some numerical examples are discussed.

Keywords

Absolute rates of decrements;rates of decrement due to cause j;uniform distribution of decrements;constant force assumption

References

  1. Shiu, E. S. W. (1987). Multiple-decrements by Riemann-Stieltjes integration, Actuarial Research Clearing House, 1, 1-4
  2. London, D. (1997). Survival Models and Their Estimation, ACTEX Publications
  3. Daniel, J. W. (1993). Multiple-decrement models and corresponding conditional single-decrement models, Actuarial Research Clearing House, 1, 229-237
  4. Carriere, J. F. (1994). Dependent decrement theory, Transactions of Society of Actuaries, 46, 45-74
  5. Bowers, N. L., Jones, D. A., Gerber, H. U., Nesbitt, C. J. and Hickman, J. C. (1997). Actuarial Mathematics, Society of Actuaries
  6. Apostol, T. M. (1974). Mathematical Analysis, Addison-Wesley
  7. Golbeck, A. L. (1986). Probabilistic approaches to current life table estimation, American Statistical Association, 40, 185-190

Cited by

  1. On survival assumptions between integer ages in the theory of competing risks vol.45, pp.4, 2016, https://doi.org/10.1016/j.jkss.2016.05.006
  2. Study on Assumptions for Fractional Ages in Life Insurance vol.25, pp.1, 2012, https://doi.org/10.5351/KJAS.2012.25.1.001
  3. Conversion between Decrement Models using Cubic Spline vol.26, pp.3, 2013, https://doi.org/10.5351/KJAS.2013.26.3.549