A Closed-Form Solution of the Multi-Period Portfolio Choice Problem for a Quadratic Utility Function

In the present paper, we derive a closed-form solution of the multi-period portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different time points is needed and no assumption on the distribution is imposed. All expressions are presented in terms of the conditional mean vectors and the conditional covariance matrices. If the multivariate process of the asset returns is independent it is shown that in the case without a riskless asset the solution is presented as a sequence of optimal portfolio weights obtained by solving the single-period Markowitz optimization problem. The process dynamics are included only in the shape parameter of the utility function. If a riskless asset is present then the multi-period optimal portfolio weights are proportional to the single-period solutions multiplied by time-varying constants which are depending on the process dynamics. Remarkably, in the case of a portfolio selection with the tangency portfolio the multi-period solution coincides with the sequence of the simple-period solutions. Finally, we compare the suggested strategies with existing multi-period portfolio allocation methods for real data.Comment: 38 pages, 9 figures, 3 tables, changes: VAR(1)-CCC-GARCH(1,1) process dynamics and the analysis of increasing horizon are included in the simulation study, under revision in Annals of Operations Researc

Çok kriterli portfolyo optimizasyonu.

Portfolio optimization is the problem of allocating funds between available investment options in the financial market. This thesis develops several approaches to multicriteria portfolio optimization. The use of multiple criteria is justified by demonstrating their effects on decision and objective spaces of the problem. The performance of a genetic algorithm with two and three criteria is studied; and a preference-based genetic algorithm to solve portfolio optimization with complicating constraints is developed. Furthermore, stochastic programming is used to handle multi-period problems, and several issues are studied with this approach. Efficient market hypotheses, random walk and single index models are discussed in the context of scenario generation for the Turkish Stock Market. An interactive approach to stochastic programming-based portfolio optimization is also developed to guide the decision maker toward preferred solutions. The approaches are experimented with and demonstrated using stocks from the Turkish Stock Market.Ph.D. - Doctoral Progra