Valuation of Reverse Mortgages Using Stochastic Programming Models

Abstract

The aging society problems spread all around the world in recent years. The elders face economic impact and financial difficulties after they retired. The reverse mortgage (RM) programs are then introduced to alleviate the elders' income shortages in many countries. In this paper we propose a bi-objective stochastic programming model to evaluate the fair payment of RM programs. We use Lee-Carter model (1992), CIR-SR model (1985), and Geometric Brownian motion model to forecast mortality, interest rates, and house prices, respectively. Numerical tests and sensitivity analyses using data from Taiwan are also performed to demonstrate the valuation procedure of RM programs.老齡化問題近年來已在全世界迅速蔓延。老年人在退休後面臨嚴重的經濟及財務問題，許多國家則實施逆向抵押貸款政策以減緩老年人缺乏收入所造成的問題。本文提出一個雙目標動態規劃模型，用以估算逆向抵押貸款之合理給付。並以臺灣主要城市之資料為基礎，分別估計死亡率、利率、以及房屋價格，以演示逆向抵押貸款之評價過程。