Portfolio selection via replicator dynamics and projections of indefinite estimated covariances

Replicator dynamics are an increasingly popular device for obtaining (local) solutions of considerably high quality to so-called standard quadratic optimization problems, which consist of finding maxima of (possibly indefinite) quadratic forms over the standard simplex. In the simplest version of portfolio selection, the quadratic form is theoretically negative-semidefinite, so that any local solution automatically is a global one. However, if it comes to more realistic set-ups, then (i) no market portfolio is available, so that one ends up with an indefinite theoretical problem, (ii) estimated covariance matrices modelling risk may be indefinite also. This paper deals with both problems in a different way: (i) will be solved via escape steps to avoid low-quality local solutions while (ii) is dealt with by several projection strategies which convert the indefinite estimated covariance matrix into a positive-semidefinite one. (author's abstract)