Math Sciences

Abstract Several exponential bounds are derived by means of the theory of large deviations for the convergence of approximate solutions of stochastic optimization problems. The basic results show that the solutions obtained by replacing the original distribution by an empirical distribution provides an effective tool for solving stochastic programming problems.

Abstract We present a tracking model for asset allocation that tracks desired investment goals. The model is shown to be optimal with respect to an investor's 'regret distribution', the cumulative distribution of the difference between the revenue under perfect foresight and that possible without foresight. Relationships with Markowitz mean/variance models are also explored.

Abstract Finding portfolios with given mean return and minimal lower partial mean or variance, two risk criteria of interest in the theory of optimal portfolio selection, is a stochastic linear-quadratic program that can be converted to a large-scale linear or quadratic program when the asset returns are finitely distributed. These efficient frontiers can be computed on presently available platforms for problems of reasonable size; we discuss our experience with a problem involving one thousand assets. Asymptotic statistics for stochastic ...