Abstract
The intent of the home reversion plan for retired homeowners in United Kingdom is to help house-rich but cash-poor seniors by the way of releasing their home equity into cash so as to meet living expenses and continue to enjoy the right to live in their home until their death. We present multiple finite state Markov models to price the continuous annuities of insurance policies relevant to home reversion plan for a pair of insureds (meaning husband and wife). Our modeling assumes that the home value follows a geometric Brownian motion. By applying the principle of equivalent utility, we derive the partial differential equation system that the indifferent annuities satisfy under the exponential utility function, and find their explicit representations. Furthermore, we employ an explicit finite difference scheme to calculate the numerical solution and discuss the impacts of the risk aversion of insurer, the volatility of home value, and the interest rate on the annuities of home reversion plan for a couple. We observe that these results reflect our intuition.
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