Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 61895, 22 pages
doi:10.1155/JAMDS/2006/61895
Abstract
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.