A tilting algorithm for the estimation of fractional age survival probabilities

Life tables used in life insurance determine the age of death distribution only at integer ages. Therefore, actuaries make fractional age assumptions to interpolate between integer age values when they have to value payments that are not restricted to integer ages. Traditional fractional age assumptions as well as the fractional independence assumption are easy to apply but result in a non-intuitive overall shape of the force of mortality. Other approaches proposed either require expensive optimization procedures or produce many discontinuities. We suggest a new, computationally inexpensive algorithm to select the parameters within the LFM-family introduced by Jones and Mereu (Insur Math Econ 27:261-276, 2000). In contrast to previously suggested methods, our algorithm enforces a monotone force of mortality between integer ages if the mortality rates are monotone and keeps the number of discontinuities small.