Probabilistic solutions for a class of deterministic optimal allocation problems
| Autor: | Jan Dhaene, Sheung Chi Phillip Yam, Ka Chun Cheung, Yian Rong |
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| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Class (set theory)
Mathematical optimization Optimization problem HETEROGENEOUS PORTFOLIO COMONOTONICITY Mathematics Applied Stop-loss transform 01 natural sciences VARIABLES 0101 mathematics Constrained optimization Budget constraint Mathematics Optimal allocation Science & Technology Applied Mathematics Comonotonicity 010102 general mathematics Probabilistic logic 010101 applied mathematics Computational Mathematics Physical Sciences Resource allocation Convex function Random variable |
| Popis: | © 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. ispartof: Journal Of Computational And Applied Mathematics vol:336 pages:394-407 status: published |
| Databáze: | OpenAIRE |
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