Optimal investment policy

Abstract

This paper deals with a system of two linear ordinary differential equations representing the rate of change with respect to time of the liquid and the non-liquid assets of a company. These equations involve a control variable that gives the rate at which the company invests. The objective is to find the investment policy that will maximize the minimal value taken by the liquid assets, assuming that the company remains in business forever. The actual value of the minimal liquid assets obtained by using this optimal policy is also determined.