We use a mean-variance model to analyze the problem of decentralized
portfolio management. We find the solution for the optimal portfolio
allocation for a head trader operating in <i>n</i> different
markets, which is called the optimal centralized portfolio. However, as
there are many traders specialized in different markets, the solution to the
problem of optimal decentralized allocation should be different from the
centralized case. In this paper we derive conditions for the solutions to be
equivalent. We use multivariate normal returns and a negative exponential
function to solve the problem analytically. We generate the equivalence of
solutions by assuming that different traders face different interest rates
for borrowing and lending. This interest rate is dependent on the ratio of
the degrees of risk aversion of the trader and the head trader, on the
excess return, and on the correlation between asset returns.
Portfolio allocation under asymmetric dependence in asset returns using local Gaussian correlations
