PRICING AN INSURANCE PRODUCT THAT INTEGRATES REVERSE MORTGAGE WITH LONG-TERM CARE INSURANCE

We derive in this article the pricing formula for an insurance product that integrates reverse mortgage with long term care. This pricing is based on the principle of balance between the mean gain and mean payment. We compute the expected gain and the expected payment respectively under the continuous and discrete framework. Here, we assume that the dynamics of the housing price is driven by the Black-Scholes model and the interest rate is driven by the Ornstein-Uhlenbeck process. With these assumptions, we present closed-form formulas for the growing perpetuity annuity, the state annuity, and the constant annuity. Furthermore, we discuss the monotonicity property of the annuities, lump sum, and annuity payment factors with respect to the parameters of housing price, interest rate model, and the age of the insured. We present the numerical results for the lump sum, the annuity, and the annuity payment factors, and analyze the sensitivity with respect to the above parameters. We also show that the mean return of housing price has the dominating influence on the lump sum and annuity