PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

ESTIMATING THE WORKERS COMPENSATION TAIL 641In effect, in Table 9.1, projected annual medical costs for eachfuture year are estimated via a Markov chain simulation model.The state space consists of two outcomes from each trial: (1)the claimant does not die during a given future DY, or (2) theclaimant dies during that DY. The transition probabilities in thismodel are simply the (1 ¡ q x )andq x values from a mortality table.The outcome of any trial depends at most upon the outcomeof the immediately preceding trial and not upon any other previousoutcome. Death is an “absorbing” state, since one cannottransition out of it.An assumed rate of medical cost escalation of 9% per year isapplied to the prior year’s payments if the claimant lives throughoutthe year. Otherwise, if the claimant dies during the year, projectedmedical payments for the year are still shown, after whichmedical losses drop to zero for every future year of development.While projected medical payments may arguably be onlyfor half a year, assuming the average claimant dies in the middleof the final year of development, in reality medical costs are oftenhigher during the year of death. Thus assuming a full year’sworth of medical payments is a reasonable assumption.For each trial, total projected future payments from the cellat the bottom right are recorded and confidence levels for thereserve can be derived from a ranking of all of the simulated totalreserve estimates. If this is done for a single claim, the resultingprobability distribution closely conforms to that described in thefirst paragraph of this section.Simulating the variability of the MPD reserve for unreportedclaims is naturally more complicated. First, the total numberof IBNR claims should be represented by a Poisson (or similar)distribution. Then census data of the age at injury of recentclaimants can be used to randomly generate these ages for unreportedclaimants. Then additional rows can be added to Table9.1 to further simulate future payments for each unreportedclaimant. The degree of variability of the MPD reserve for unreportedclaimants is exceptionally high, because some of those