Math. Meth. Oper. Res. (2006) 63: 151–168 DOI 10.1007/s00186-005-0020-x ORIGINAL ARTICLE U. C ¸ akmak · S. ¨ Ozekici Portfolio optimization in stochastic markets Received: Febraury 2005 / Revised version: March 2005 / Published online: 6 October 2005 © Springer-Verlag 2005 Abstract We consider a multiperiod mean-variance model where the model param- eters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure. Keywords Portfolio optimization · Stochastic market · Dynamic programming · Mean-variance models · Efficient frontier 1 Introduction Portfolio management deals with the allocation of wealth among different invest- ment opportunities in a market, considering investor’s preferences on risk and return. Determination of the investment policy is a rather complex problem that is affected by many factors. The classical mean-variance model of Markowitz (1952) is undoubtedly the most celebrated one within the vast area of portfolio manage- ment. In this paper, we consider a multiperiod model where the investor chooses a portfolio at the beginning of each period depending on the state of a stochastic market that affects both the mean vector and the covariance matrix of the asset U. C ¸ akmak School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA S. ¨ Ozekici (B ) Department of Industrial Engineering, Ko¸ c University, 34450 Sarıyer- ˙ Istanbul, Turkey E-mail: sozekici@ku.edu.tr