Measuring and analyzing volatility risk in disability income
Disability Income (DI) is important to both policyholders and insurance companies. Companies however have experienced significant losses in their DI business because of anti-selection and volatility risk. In this dissertation, we define and measure volatility risk in terms of adequacy of DI claim reserves. Using stochastic simulation, we quantify the volatility risk under more than 5,000 plan designs with 1,000 simulations per design; Based on the simulation results, we provide a regression method to develop risk adjusted claim reserves from base claim reserves. In special cases, we prove some theorems about volatility risk and properties of DI termination rates. We use complete expectation time of staying disabled to obtain a simple approximation and give an analytic approximation of volatility risk. We also apply statistical tests of the closeness of fit of the regression and analytical results to the 'true' volatility risk. Finally, we discuss the applications of our methods to the development of active life reserves, risk adjusted premiums (DI pricing problem) and applications to other 'risky' forms of insurance.
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