Theory of Dynamic Portfolio Choice for Survival Under Uncertainty

This paper develops a discrete time theory of dynamic optimization whre the objective is to maximize the long run probability of survival through risk portfolio choice over time. There is an exogenously given minimum withdrawal (subsistence consumption) requirement and the agent survives only if his wealth is large enough to meet this requiremnet every time period over an infinite horizon. The agent is endowed with an initial wealth. Every time period he withdraws a part of the current wealth and allocates the rest between a risky and a risk-less asset. Assuming the returns on the risky asset to be i.i.d. with continuous density, the existence of a stationary optimal policy and the functional equation of dynamic programming are established. This is used to characterize the maximum survival probability and the stationary optimal policies. The stationary optimal policies exhibit variable risk preference ranging from extreme "risk loving" behavior for low levels of wealth to "risk-averse" behavior for high levels of wealth.