Author:

Keywords:

Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, Optimal allocation, Constrained optimization, Comonotonicity, Stop-loss transform, HETEROGENEOUS PORTFOLIO, COMONOTONICITY, VARIABLES, 0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, 0906 Electrical and Electronic Engineering, Numerical & Computational Mathematics, 4613 Theory of computation, 4901 Applied mathematics, 4903 Numerical and computational mathematics

Abstract:

© 2018 Elsevier B.V. We revisit the general problem of minimizing a separable convex function with both a budget constraint and a set of box constraints. This optimization problem arises naturally in many resource allocation problems in engineering, economics, finance and insurance. Existing literature tackles this problem by using the traditional Kuhn–Tucker theory, which leads to either iterative schemes or yields explicit solutions only under some special classes of convex functions owe to the presence of box constraints. This paper presents a novel approach of solving this constrained minimization problem by using the theory of comonotonicity. The key step is to apply an integral representation result to express each convex function as the stop-loss transform of some suitable random variable. By using this approach, we can derive and characterize not only the explicit solution, but also obtain its geometric meaning and some other qualitative properties.