We have determined that the most appropriate approach to construct such a simulator is by modeling the loss process at the claim transaction level, rather than by modeling statistics of the loss process such as loss triangles. We describe the loss process in terms of the distributions of
(a) number of incurred losses, as a function of time and exposure,
(b) size of each loss, i.e. severity, from the viewpoint of the claimant,
(c) the probability that the insurer will be liable for payment of the loss,
(d) the effect of deductibles, limits, etc., on the amount for which the insurer is liable,
(e) the lag between the dates a claim is incurred and is reported,
(f) the lag between claim reporting and payment,
(g) any “error” in payment amount that may require later correction, usually a subrogation or recovery,
(h) the lag between the original payment and receipt or payment of any later adjustment,
(i) the value assigned to the case reserve at first notice of each loss,
(j) the lag from one valuation of each loss to the next during the period between reporting and payment, and
(k) the error between the valuation of a loss and its true value at various points in time between reporting and payment.
As described, this model applies to insurance coverages of the kind that typically involve losses with a single payment followed by a single recovery, such as automobile physical damage. We recognize that there is a slight possibility of multiple recoveries but this has been left out of the model for reasons of simplicity. We have extended the model to apply to coverages that involve losses with multiple periodic payments, such as Workers’ Compensation indemnity, and random multiple payments (such as Medical Expense). We have also extended the model to accommodate mixtures of losses with different characteristics, such as are often found in loss triangles, to accommodate correlated distributions such as size of loss and lag to payment, and to accommodate variation in parameters over time, both deterministic and random.