Abstract

In this thesis we consider a financial market model consisting of a bond with deterministic growth rate, and d risky assets, governed by Brownian motion with drift. We can shift money from one asset to the other without loss of capital. Optimal investment and consumption (spending) decisions are examined for different types of investors with various criteria for optimality. An investor’s level of satisfaction with any amount of wealth is measured by a utility function. The problem has been solved by Merton [4] and others for the small investor with no transaction costs. Here we suppose the investor is large, i.e., his strategy has an effect on the asset price evolution. The approach parallels th a t taken by Cvitanic and Karatzas [5] for constrained portfolios. The theorems therein are adjusted appropriately to account for the investor’s effect on prices instead of constraining the portfolios as Cvitanic and Karatzas do. As in Cvitanic and Karatzas [5], Karatzas et al.[6] and several others duality theory and martingale methods are introduced to prove the existence of the optimal portfolio which maximises the expected final utility. An algorithm is suggested to find this portfolio under certain market conditions.