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

ESTIMATING THE WORKERS COMPENSATION TAIL 635in keeping with the standard definition of the expected value oftotal incurred.The total case reserve based on this third approach is dramaticallyhigher than that derived from the second approachbecause the cumulative paid amounts associated with death atages beyond the claimant’s expected year of death are givenmore weight, due to the compounding effects of medical costescalation.In Tables 8.1A and 8.1B the medical case reserve for thehypothetical PD claimant is calculated for the second and thirdmethods. For the second method, Projected Payments ThroughExpected Year of Death, the cumulative payments from Column(F) at the end of the expected year of death (at age 75) yieldsthe estimate of $1,689,000.For the third method, each row is treated as a different scenario,with its probability of occurrence shown in Column (C).These probabilities are the weights applied to the estimates ofcumulative medical payments in Column (F) to obtain the componentsof the expected total payout in Column (G) that arecumulated in Column (H). Hence, the expected value of thecase reserve is the bottom number in Column (H) in Table 8.1B($2,879,000).The distribution of deaths by age of death (Column (C))would be the same as the distribution of the different scenariosfor the indemnity case reserve, since incremental indemnitypayments are not generally subject to inflation. Figure 8.1 illustratesthe shift in the distribution of the different scenarios forthe medical case reserve [Column (I) decumulated, or Column(G) divided by Total in Column (H)], due to the effects of compoundingmedical cost escalation in giving more dollar weightto scenarios where the claimant lives beyond his expected yearof death.