Optimal Portfolio Selection In A Log-normal Market When The Investor's Utility-function Is Logarithmic

The paper analyzes the portfolio choice problem when the investor has logarithmic utility of wealth and asset returns have a multivariate lognormal distribution. It is shown that there exists a surrogate problem (objective function) which has the same structural properties as those found for the original problem. The surrogate problem involves the minimization of quadratic form and under a number of circumstances the surrogate problem yields an optimal solution identical to that of the original problem. The optimal solutions of the surrogate and original problems converge toward each other in a time-asymptotic sense.