• The Korean Journal of Applied Statistics
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• v.21 no.5
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• pp.739-754
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• 2008

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.

• The Korean Journal of Applied Statistics
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• v.26 no.3
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• pp.549-568
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• 2013

This paper discusses conversion methods between multiple decrement models and associated single decrement models. One of most popular assumptions on fractional age is UDD(uniform distribution of decrement) or constant force of mortality in actuarial practice. Instead of these assumptions, this paper suggests cubic spline interpolation to approximate the distribution of fractional age with the continuous force of decrements. Conversion formulas are derived. The comparisons of these two methods based on the numerical data show that the cubic spline interpolation approach is more accurate.