Point-to-point stochastic control of a self-financing portfolio

Abstract

This paper aims at computing optimal control policies to drive a self-financing portfolio of financial assets from a given initial financial state to a final state in a given time horizon such that for the first case, the functional portfolio financial risk is minimized and, for the second case, the functional portfolio profit is maximized. The optimal control policies are the optimal investment allocation processes, the optimal state process is the optimal investor’s wealth process, also called the system response to the input control and is obtained by solving the combined system of differential equations formed by the state and costate system of differential equations derived and extracted from Pontryagin’s Minimum Principle. Computational simulations are provided to show the effectiveness and the reliability of the approach.