Mean-risk optimization for index tracking

This paper presents an analysis of the tracking problems of multiple indices with multidimensional performance criterion consisting of mean wealth and the tracking errors. We evaluate the performance of portfolios via the vector inequalities defined by convex cones, which enable us to describe various preference relations for investors. In Brownian market models with deterministic coefficients, we completely determine the set of efficient portfolios as well as the efficient frontier in our context. As a product of our analysis, we exhibit a version of Tobin's mutual fund theorem.