Optimal portfolio selection in finite state economy

The paper briefly characterizes the early contributions to the modern portfolio theory and presents a static approach to the optimal portfolio choice in a complete market without transaction costs and a incomplete market with transaction costs. Mean-variance portfolio theory addresses the investor's asset selection problem for an investment horizon of one period. Progress in portfolio theory came as financial economists relaxed this restrictive assumption. In so doing they faced two interrelated consumer or household problems that are known as the consumption - saving decision and the portfolio selection problem. The relaxation of the single period assumption proceeded along two lines: firstly, in discrete time multiperiod models, and secondly, in continuous time models. In the paper the discrete, time intertemporal portfolio selection problem is treated. The focus here is on the optimal portfolio choice behaviour of an individual investor who takes as given an arbitrage-free process for asset prices. The presented approach to the optimal portfolio choice problem of an investor who maximizes the expected utility of his lifetime consumption do not use the traditional dynamic programming approach to characterize a solution to this problem, but reduces die dynamic problem to a static one and leads to an elegant characterization of the optimal portfolio choice problem. The paper shows that the finite state framework is quite useful in bringing forward important economic insights related to the portfolio choice question.