Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 61895, 22 pages

Delegated dynamic portfolio management under mean-variance preferences

Coskun Cetin

Department of Mathematics, Whittier College, Whittier 90608-0634, CA, USA

Received 24 January 2006; Revised 12 March 2006; Accepted 7 June 2006

Copyright © 2006 Coskun Cetin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a complete financial market with deterministic parameters where an investor and a fund manager have mean-variance preferences. The investor is allowed to borrow with risk-free rate and dynamically allocate his wealth in the fund provided his holdings stay nonnegative. The manager gets proportional fees instantaneously for her management services. We show that the manager can eliminate all her risk, at least in the constant coefficients case. Her own portfolio is a proportion of the amount the investor holds in the fund. The equilibrium optimal strategies are independent of the fee rate although the portfolio of each agent depends on it. An optimal fund weight is obtained by the numerical solution of a nonlinear equation and is not unique in general. In one-dimensional case, the investor's risk is inversely proportional to the weight of the risky asset in the fund. We also generalize the problem to the case of multiple managers and provide some examples.