Title

Stochastic modeling of long-term care insurance

Date of Completion

January 2001

Abstract

One of the key developments in modern actuarial science has been the introduction of stochastic models. This is necessitated by the design complexity of products being offered in today's marketplace and the many variables that can impact the financial performance of these products. Most of the stochastic modeling has focused on the variables impacting the asset side of an insurance operation like market returns, asset defaults and interest rates. In this thesis, a stochastic model is developed for the Long-Term Care (LTC) Insurance product, focusing on the liability risks like mortality, morbidity and lapse behavior. The model tries to measure the pricing volatility of the LTC rider insurance as well as the stand-alone product, caused by the volatility in these liability risks. The stochastic process governing the model is a Markov Chain process. We first discuss the traditional deterministic pricing of Long-Term Care Insurance. An algorithm is proposed to simulate the LTC insurance process. In addition, a regression model is developed to estimate the volatility risk and thus derive a deterministic approximation to the risk-adjusted net single and level premiums. The robustness of the regression model is tested against the full simulation model, under different assumptions and changes in product design. ^