Consumption and Portfolio Optimisation at the End of the Life-Cycle

The thesis' focus is on the consumption/portfolio optimisation and the optimal annuitisation decision of a pensioner in a continuous time setting. Technically, this involves solving a combined optimal stopping and optimal control problem (COSOCP). The retiree faces the crucial question of how much to consume and how much to invest in the risky asset (financial market risk). This creates the optimal control aspect of the COSOCP. The second source of uncertainty is the pensioner's longevity risk, which is why we include an annuity market. The pensioner has to find the optimal time to annuitise his wealth. This constitutes the optimal stopping aspect of the COSOCP. The task of finding the pensioner's optimal consumption, asset allocation and annuity decision rule leads to the interesting interplay of optimal control theory, optimal stopping theory and finally, mortality and bequest issues.