Multiple-Random-Payment Model  


The multiple-random-payments model approximates the development pattern of coverages such as Medical Payments, where each occurrence is followed by a random number of reimbursable incurred expenses.  Each expense is followed by one reporting and one payment.  The final expense payment (which may or may not be the final expense incurred) is followed by zero or one recovery or other adjustment to the total of all previous payments.  

The number of reimbursable expenses per claim is assumed to follow a geometric distribution or a multinomial distribution specified by the user.

The severity parameters describe the distribution of severities for each individual expense, except that the deductible and maximum apply to all expenses in aggregate.  There is a single trend factor (actually annual trend rate) applied to each expense through its incurral date, and there is decay factor allowing the user to specify a declining mean from one expense to the next expense arising from the same claim.

Case reserves are assumed to be revalued at each payment date.  Their adequacy is measured relative to all expenses that have been or will be incurred but have not yet been paid, subject to a minimum that allows a reserve to be carried between the last payment and the recovery date.  The "P(2 sig dig)" entry represents the probability that a case reserve will be estimated to a nearby "round" number -- in this case rounding to two significant digits -- rather than its exact value.

Recoveries are modeled as one-time adjustments to correct errors in the original amounts paid.  For this purpose each amount paid is treated as an adequacy factor times the actual severity after application of the deductible and the maximum.  Payment errors are reflected in the distribution of this factor less 1.00.  In particular, if the adequacy factor is greater than 1.00, the initial payment will be too great and will produce a future recovery, represented as a negative payment.  The simulator generates both the original overpayment or underpayment, spread uniformly across all payment dates, and the later recovery or adjustment.


Modeling Process