Optimal investment and consumption strategy for a retiree under stochastic force of mortality

With an increase in the self-driven retirement plans during past few decades, more and more retirees are managing their retirement portfolio on their own. Therefore, they need to know the optimal amount of consumption they can afford each year, and the optimal proportion of wealth they should invest in the financial market. In this project, we study the optimization strategy proposed by Delong and Chen (2016). Their model determines the optimal consumption and investment strategy for a retiree facing (1) a minimum lifetime consumption, (2) a stochastic force of mortality following a geometric Brownian motion process, (3) an annuity income, and (4) non-exponential discounting of future income. We use a modified version of the Cox, Ingersoll, and Ross (1985) model to capture the stochastic mortality intensity of the retiree and, subsequently, determine a new optimal consumption and investment strategy using their framework. We use an expansion method to solve the classic Hamilton-Jacobi-Bellman equation by perturbing the non-exponential discounting parameter using partial differential equations.