On the dual of the solvency cone

被引：2

作者：

Loehne, Andreas ^{[1
]}

Rudloff, Birgit ^{[2
,3
]}

机构：

[1] Univ Halle Wittenberg, Dept Math, D-06099 Halle, Saale, Germany

[2] Princeton Univ, Dept Operat Res & Financial Engn, Princeton, NJ 08544 USA

[3] Bendheim Ctr Finance, Princeton, NJ 08544 USA

来源：

DISCRETE APPLIED MATHEMATICS | 2015年 / 186卷

关键词：

Dual cone; Transaction costs; Degree sequences; Optimal flow; Networks with gains; TRANSACTION COSTS;

D O I：

10.1016/j.dam.2015.01.030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：176 / 185

页数：10

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