Retirement Spending under a Habit Formation Model

In the thesis we consider the problem of optimizing lifetime consumption under a habit formation model. Our work differs from previous results, because of incorporating mortality and pension income, using a fixed rather than a variable asset allocation, and adopting habit into the utility multiplicatively rather than additively, Lifetime utility of consumption makes the problem time inhomogeneous, because of the effect of ageing. Considering habit formation means increasing the dimension of the stochastic control problem, because one must track smoothed-consumption using an additional variable, habit. Including exogenous pension income means that we cannot rely on a kind of scaling transformation to reduce the dimension of the problem as in earlier work, therefore we solve it numerically, using a finite difference scheme and then using a static programming approach. We also explore how consumption changes over time based on habit if the retiree follows the optimal strategy in the first part and a greedy strategy in the second part of the thesis. Also we explore how the optimal consumption and asset allocation change when pension varies. Finally, we answer the question of whether it is reasonable to annuitize wealth at the time of retirement or not by varying parameters, such as asset allocation and the smoothing factor.