Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation

Abstract

The mean-variance formulation by Markowitz in the 1950s paved a foundation for modern portfolio selection analysis in a single period. This paper considers an analytical optimal solution to the mean-variance formulation in multiperiod portfolio selection. Specifically, analytical optimal portfolio policy and analytical expression of the mean-variance efficient frontier are derived in this paper for the multiperiod mean-variance formulation. An efficient algorithm is also proposed for finding an optimal portfolio policy to maximize a utility function of the expected value and the variance of the terminal wealth. Copyright Blackwell Publishers Inc. 2000.

Optimal mean-variance portfolio selection

“…The methodology in these papers relies upon the results on multi-index optimisation problems from the paper by Reid and Citron [17] and is more involved (in comparison with the simple conditioning combined with a double application of Lagrange multipliers as done in the present paper). In particular, the results of [10] and [24] do not establish the existence of statically optimal controls in the problems (2.4)-(2.6) although they do derive their closed form expressions in discrete and continuous time respectively. In this context it may be useful to recall that the first to point out that nonlinear dynamic programming problems may be tackled using the ideas of Lagrange multipliers was White in his paper [23].…”

Multiperiod mean-variance efficient portfolios with endogenous liabilities

“…In particular, following Li and Ng (2000), Leippold et al (2004) prove that (i) any solution of P (1) is also a solution of P (2) and (ii) if w * is a solution of P (2) for given (ψ * , θ), then it is also a solution for P(1), if the condition…”

“…Li, Zhou and Lim (2002) study the solutions of a continuous time mean-variance portfolio optimization problem under short-selling constraints on stocks. Their approach adopts the embedding technique first applied by Li and Ng (2000) in a discrete-time mean-variance model. 3 Models that include explicitly liabilities in a static Markowitz-type optimization were proposed already in the early nineties; see for instance Sharpe and Tint (1990), Elton and Gruber (1992), Leibowitz, Kogelman and Bader (1992), and later Keel and Müller (1995).…”

Optimal robust mean-variance hedging in incomplete financial markets

“…In recent paper of Li and Ng [22] the concept of Markowitz's mean-variance formulation for finding the optimal portfolio policy and determining the efficient frontier in analytical form has been extended to multiperiod portfolio selection.…”