An Alternative Approach to Portfolio Selection Problem via Stochastic Differential Delay Equations

This paper presents an alternative method to the portfolio selection problem. The central hypothesis is that the historical performance of the market can not be ignored. Consequently, we suppose that the price dynamics of any asset will be described by a stochastic differential delay equation: dP(t) = [aP(t) + bP (t − r)]dt + P(t)dW(t). We will illustrate our model by a numerical example and will compare the results with those derived from the classical model of Markowitz.