Life-cycle investment and housing decisions with longevity annuities and reverse mortgage

We investigate optimal life-cycle consumption, investment, and housing decisions with longevity annuities and reverse mortgage. A risk-averse investor can hold financial assets, such as cash, bonds, and stocks, and can invest in housing, through renting and purchasing. Variable-rate mortgages are available. At retirement, the investor can release his housing equity through a reverse mortgage product. Longevity annuities are also available to support his income at advanced ages. We use multi-stage stochastic programming to solve the optimization problem numerically. Our numerical results show that longevity annuities can enhance non-housing consumption in retirement and the proceeds from reverse mortgage may raise not only housing and non-housing consumption in retirement but also non-housing consumption prior to retirement. Reverse mortgage also changes housing preference from renting to owning with a lower regular mortgage debt. Longevity annuities can help different risk-averse investors choose a suitable consumption stream in retirement. When social security cannot guarantee a high level of the replacement ratio, our model finds that longevity annuity and reverse mortgage can prevent housing and non-housing consumption drops in retirement. The housing ownership preference over rental however becomes more intense.