Stochastic target hitting time and the problem of early retirement

We consider a problem of optimal control of a "retirement investment fund" over a finite time horizon with a target hitting time criteria. That is, we wish to decide, at each stage, what percentage of the current retirement fund to allocate into the limited number of investment options so that a decision maker can maximize the probability that his or her wealth exceeds a target x prior to his or her retirement. We use Markov decision processes with probability criteria to model this problem and give an example based on data from certain options available in an Australian retirement fund.