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An Algorithm For Calculating The Set Of Superhedging Portfolios In Markets With Transaction Costs

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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)

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.

Suggested Citation

  • Andreas Löhne & Birgit Rudloff, 2014. "An Algorithm For Calculating The Set Of Superhedging Portfolios In Markets With Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-33.
  • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:02:n:s0219024914500125
    DOI: 10.1142/S0219024914500125
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    Citations

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    Cited by:

    1. c{C}au{g}{i}n Ararat & Zachary Feinstein, 2019. "Set-Valued Risk Measures as Backward Stochastic Difference Inclusions and Equations," Papers 1912.06916, arXiv.org, revised Sep 2020.
    2. Birgit Rudloff & Firdevs Ulus, 2019. "Certainty Equivalent and Utility Indifference Pricing for Incomplete Preferences via Convex Vector Optimization," Papers 1904.09456, arXiv.org, revised Oct 2020.
    3. Emmanuel Lepinette, 2020. "Random optimization on random sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 159-173, February.
    4. Çağin Ararat & Andreas H. Hamel & Birgit Rudloff, 2017. "Set-Valued Shortfall And Divergence Risk Measures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(05), pages 1-48, August.
    5. Zachary Feinstein & Birgit Rudloff, 2018. "Time consistency for scalar multivariate risk measures," Papers 1810.04978, arXiv.org, revised Jul 2019.
    6. Alet Roux & Zhikang Xu, 2019. "Optimal investment and contingent claim valuation with exponential disutility under proportional transaction costs," Papers 1909.06260, arXiv.org.
    7. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Jun 2020.
    8. Zachary Feinstein & Birgit Rudloff, 2015. "A recursive algorithm for multivariate risk measures and a set-valued Bellman's principle," Papers 1508.02367, arXiv.org, revised Jul 2016.
    9. Zachary Feinstein & Birgit Rudloff, 2015. "A Supermartingale Relation for Multivariate Risk Measures," Papers 1510.05561, arXiv.org, revised Jan 2018.

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