VOLUNTARY RETIREMENT AND OPTIMAL CONSUMPTION IN A STOCHASTIC MORTALITY ENVIRONMENT

My objective is to analyze a life cycle model in which an individual ages in a stochastic and non-linear fashion, in order to determine his optimal time to retire, and his plan for consuming optimally over the entire lifetime. Stochasticity is incorporated into the model using mortality rates that depend on biological age as well as calendar age. Biological age depends upon the status of the individual’s health. Unlike calendar age, which always moves forward, biological age can occasionally move against the natural clock time, so individuals with the same birth dates may age at different rates. A rational retirement decision should be based on both ages. Huang, Milevsky and Salisbury (2017) used biological age to analyze an individual’s optimal retirement spending. This thesis is an extension of their work. In my model there is labor income in the pre-retirement period. For post-retirement life there may be a pension to supplement retirement savings. I use a Cobb-Douglas utility function that provides a fixed multiplicative bonus to the utility of consumption in retirement. I derive and solve Hamilton Jacobi Bellman (HJB) equations in the above Cobb-Douglas utility framework. I show among that consumers at same wealth level; the older consumer prefers to retire at a lower biological age while a younger consumer prefers to keep earning labor income until later biological ages. As per the common intuition, high wealth levels drive people to retire young and in better health status. The model predict some fascinating effects of the volatility of biological age on retirement curves. At lower wealth levels, high volatility drives less healthier people to retire later. The model with deterministic hazard rates also depicts an interesting non-uniqueness behavior in the wealth dynamics curves. Below a certain initial wealth level people slowly spend money over time but never retire while above this wealth they save for retirement and eventually retire. Then there is a wealth level beyond which they never enter the labor force. Also, over a fair range of age, health status and wealth, my results provide some reliable guidance for a to-be pensioner. For a moderately risk averse consumer with calendar age and biological age within a modest range around 65 years and who expects to have an exogenous pension of 40% of his annual labor income upon retirement, if he has savings equal to almost double the amount of his annual labor income he can consider retirement.