UTILITY INDIFFERENCE PRICING OF PRODUCTS INTEGRATING REVERSE MORTGAGE WITH LONG-TERM CARE INSURANCE UNDER A LEVY PROCESS FINANCIAL MARKET

We study, in this article, the indifference pricing of the continuous annuity rate of insurance contract linking home reversion plan and long-term care insurance with the dynamics of home price modeled as a finite variation Levy process. The multi-state Markov model is employed to describe the states and transitions of the combined contract. The equivalent utility principle and the exponential utility are respectively chosen as the pricing rule and utility function. As for the combined policy involving a single insured and a pair of insureds, we derive the non-linear partial-integro-differential equation system that the indifference continuous annuities satisfy. We numerically investigate the solution by an explicit finite-difference scheme, and discuss how the continuous annuity benefits vary in response to the changes of the major model parameters: the risk aversion of insurer, the force of interest, the age at the start of the combined policy, volatility of home value, the jump activity rate and the upward jump probability.