Dissaving of the past via reverse mortgages

Abstract

We build a simple two-period general equilibrium model with incomplete markets which incorporates reverse market mortgages without appealing to the complicated framework required by the infinite horizon models. Two types of agents are considered: elderly agents and investors. The former are owners of physical assets (for instance housing) who will want to sell them to investors. For that end the elderly agents, who are assumed to not have any bequest motive, issue claims against physical assets they own. One of the claims issued will be interpreted as reverse mortgage (loan for seniors) and the other one as a call option written on the value of housing equity. By assuming that both the elderly agents and the investors are price takers, and by applying the generalized game approach, we show that the equilibrium in this economy always exists, providing the usual conditions on utilities and initial endowments are satisfied. We end with a remark on efficiency of the equilibrium.