We consider a complete financial market with deterministicparameters where an investor and a fund manager have mean-variancepreferences. The investor is allowed to borrow with risk-free rateand dynamically allocate his wealth in the fund provided hisholdings stay nonnegative. The manager gets proportional feesinstantaneously for her management services. We show that themanager can eliminate all her risk, at least in the constantcoefficients case. Her own portfolio is a proportion of the amountthe investor holds in the fund. The equilibrium optimal strategiesare independent of the fee rate although the portfolio of eachagent depends on it. An optimal fund weight is obtained by thenumerical solution of a nonlinear equation and is not unique ingeneral. In one-dimensional case, the investor's risk is inverselyproportional to the weight of the risky asset in the fund. We alsogeneralize the problem to the case of multiple managers andprovide some examples.
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