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Risk arbitrage and hedging to acceptability under transaction costs

Author

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  • Emmanuel Lépinette

    (Paris-Dauphine University
    Tunis-El Manar University)

  • Ilya Molchanov

    (University of Bern)

Abstract

The classical discrete-time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing convex transaction costs and assuming that increments of the portfolio process belong to the sum of a solvency set and a family of multivariate acceptable positions, e.g. with respect to a dynamic risk measure. We describe the sets of superhedging prices, formulate several no (risk) arbitrage conditions and explore connections between them. In the special case when multivariate positions are converted into a single fixed asset, our framework turns into the no-good-deals setting. However, in general, the possibilities of assessing the risk with respect to any asset or a basket of assets lead to a decrease of superhedging prices and the no-arbitrage conditions become stronger. The mathematical techniques rely on results for unbounded and possibly non-closed random sets in Euclidean space.

Suggested Citation

  • Emmanuel Lépinette & Ilya Molchanov, 2021. "Risk arbitrage and hedging to acceptability under transaction costs," Finance and Stochastics, Springer, vol. 25(1), pages 101-132, January.
    • Handle: RePEc:spr:finsto:v:25:y:2021:i:1:d:10.1007_s00780-020-00434-3
    DOI: 10.1007/s00780-020-00434-3
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    References listed on IDEAS

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    Cited by:

    1. Çağın Ararat & Zachary Feinstein, 2021. "Set-valued risk measures as backward stochastic difference inclusions and equations," Finance and Stochastics, Springer, vol. 25(1), pages 43-76, January.
    2. Emmanuel Lepinette & Duc Thinh Vu, 2024. "Coherent Risk Measure on $L^0$: NA Condition, Pricing and Dual Representation," Papers 2405.06764, arXiv.org.
    3. Ilya Molchanov & Anja Mühlemann, 2021. "Nonlinear expectations of random sets," Finance and Stochastics, Springer, vol. 25(1), pages 5-41, January.

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    More about this item

    Keywords

    Acceptance set; Risk arbitrage; Risk measure; Superhedging; Good deal; Solvency set; Random set; Transaction costs;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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