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

ESTIMATING THE WORKERS COMPENSATION TAIL 631of development are common. They are the following:1. Zero Inflation Case Reserve Based on Projected PaymentsThrough Expected Year of Death. Estimated annualmedical expenses of $5,000 per year (during thefirst full year of development) are multiplied by thelife expectancy of 40 years to obtain a case reserve of$200,000.2. Inflation Case Reserve (9%) Based on Projected PaymentsThrough Expected Year of Death. Escalating medical expensesare cumulated up through age 75, yielding a totalincurred amount of $1,689,000.Two additional methods may also be applied. Each of theseproduces much higher, and more accurate, estimates of the expectedvalue of the case reserve:3. Expected Total Payout over Scenarios of All Possible Yearsof Death. This method, described below, yields an expectedreserve of $2,879,000.4. Expected Value of Trials from a Markov Chain Simulation.This method, described in Section 9, yields an expectedreserve of $2,854,000.In applying the third method, cumulative payments are calculatedthrough each possible future year of death. Each of theseestimates represents the scenario of the claimant’s death during aspecific nth year of development. The probability of occurrenceof the nth scenario is the product of the probability the claimantwill live through all prior years of development and then die duringthe nth year of development. The expected value of the casereserve is then the weighted average of all of these estimates offinal cumulative payments, weighted by their associated probabilityof occurrence. In this example, the expected value of totalincurred is $2,879,000, which is 70.5% higher than the secondestimate. This kind of estimate is often not calculated by selfinsuredsor insurers who have only a few PD claimants. Yet it is