Periodic Payment Model


The periodic payments model approximates the development patterns of coverages such as Group Long-Term Disability or the wage-replacement provisions of Workers' Compensation, where each occurrence is followed by a random number of regular periodic payments of equal amounts or of equal amounts subject to periodic inflation adjustments.  The final payment is followed by zero or one recovery of any payments that were inadvertently made beyond the termination of disability.


The duration of payments is assumed to follow one of the usual distributions for lags except here expressed in years rather than days.  In actual practice the distribution of payment distributions depends on factors such as the claimant's age and sex, and tabular reserves are established claim by claim reflecting these factors.  CASLDS does not directly model these factors; if they are important for a particular simulation, you may set up different types or different lines for representative combinations such as males of ages 40-44, and convert an appropriate disability continuance table to a user-defined distribution of payment durations.


The size of periodic payments is typically related to salaries and may be approximated by a suitable distribution with a minimum and maximum.  There is provision for trend, affecting the payment size at time of occurrence, and for COLA factors, affecting individual claims at annual intervals following commencement of payments.


Case reserves are assumed to be revalued at each payment date, using tabular reserves based on the distribution of payment durations, but with the implied period-to-period continuance probabilities multiplied by an "adequacy factor".  This factor may be thought of as the inverse of an actual-to-expected ratio as measured from a large volume of experience.  The same adequacy factor applies at all durations.  Note that the simulated duration of a particular claim has no effect on that claim's reserve at any valuation date before termination.


Recoveries are modeled as one-time adjustments to correct errors in the original duration of payments; therefore they are small integral multiples of the payment amount, and the simulator generates both the original excess payments and the later recovery.