On the Dual of the Solvency Cone
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2014
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929222370459648 |
|---|---|
| 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 |