On the Dual of the Solvency Cone

Fuente: arXiv
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Autores principales: Löhne, Andreas, Rudloff, Birgit
Formato: Preprint
Publicado: 2014
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author Löhne, Andreas
Rudloff, Birgit
author_facet Löhne, Andreas
Rudloff, Birgit
contents A solvency cone is a polyhedral convex cone which is used in Mathematical Finance to model proportional transaction costs. It consists of those portfolios which can be traded into nonnegative positions. In this note, we provide a characterization of its dual cone in terms of extreme directions and discuss some consequences, among them: (i) an algorithm to construct extreme directions of the dual cone when a corresponding "contribution scheme" is given; (ii) estimates for the number of extreme directions; (iii) an explicit representation of the dual cone for special cases. The validation of the algorithm is based on the following easy-to-state but difficult-to-solve result on bipartite graphs: Running over all spanning trees of a bipartite graph, the number of left degree sequences equals the number of right degree sequences.
format Preprint
id arxiv_https___arxiv_org_abs_1402_2221
institution arXiv
publishDate 2014
record_format arxiv
spellingShingle On the Dual of the Solvency Cone
Löhne, Andreas
Rudloff, Birgit
Optimization and Control
Combinatorics
90C27, 05C07, 91G99
A solvency cone is a polyhedral convex cone which is used in Mathematical Finance to model proportional transaction costs. It consists of those portfolios which can be traded into nonnegative positions. In this note, we provide a characterization of its dual cone in terms of extreme directions and discuss some consequences, among them: (i) an algorithm to construct extreme directions of the dual cone when a corresponding "contribution scheme" is given; (ii) estimates for the number of extreme directions; (iii) an explicit representation of the dual cone for special cases. The validation of the algorithm is based on the following easy-to-state but difficult-to-solve result on bipartite graphs: Running over all spanning trees of a bipartite graph, the number of left degree sequences equals the number of right degree sequences.
title On the Dual of the Solvency Cone
topic Optimization and Control
Combinatorics
90C27, 05C07, 91G99
url https://arxiv.org/abs/1402.2221