A Class of Variance-Constrained Problems

A Lagrange multiplier solution procedure is developed for a class of variance-constrained problems. The method, based on the separation of the variance and an algorithm for determining the optimal value of the mean, relies on the availability of a method of solving a modified problem in which the variance operation is replaced by the generalized variance operator. It is indicated that the procedure can be used in conjunction with dynamic programming to solve a variety of variance-constrained problems which allow the consideration of adaptive strategies. The procedure is demonstrated by a simple numerical example.