AN ALGORITHM FOR CALCULATING THE SET OF SUPERHEDGING PORTFOLIOS IN MARKETS WITH TRANSACTION COSTS

Andreas Löhne () and Birgit Rudloff ()
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Andreas Löhne: Departement of Mathematics, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Germany
Birgit Rudloff: Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 02, 1-33

Abstract: We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The set of superhedging portfolios can be obtained by a recursive construction involving set operations, going backward in the event tree. We reformulate the problem as a sequence of linear vector optimization problems and solve it by adapting known algorithms. The corresponding superhedging strategy can be obtained going forward in the tree. Examples are given involving multiple correlated assets and basket options. Furthermore, we relate existing algorithms for the calculation of the scalar superhedging price to the set-valued algorithm by a recent duality theory for vector optimization problems. The main contribution of the paper is to establish the connection to linear vector optimization, which allows to solve numerically multi-asset superhedging problems under transaction costs.

Keywords: Transaction costs; superhedging; set-valued risk measures; coherent risk measures; algorithms; conical market model; vector optimization; geometric duality; 91B30; 46A20; 46N10; 26E25; 90C29; 46N10; 26E25 (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations: View citations in EconPapers (19)

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DOI: 10.1142/S0219024914500125

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