Optimal Annuitization with Early Retirement : A Mathematical Theory

We develop a full mathematical theory in a quantitatively focused study especially for optimal annuitization with early retirement. Analytically tractable optimal consumption/investment strategies and wealth process are obtained with mandatory retirement on a finite date. Compared to the standard retirement literature without mandatory retirenemt, there is a notion of aging, where time plays an explicit role in the consumption/investment decisions and wealth accumulation for optimal annuitization via an irreversible choice of early retirement time. We also thoroughly investigate various mathematical properties of variational inequality associated with early retirement for optimal annuitization before finite-horizon mandatory retirement