Risk arbitrage and hedging to acceptability under transaction costs

Emmanuel Lépinette () and Ilya Molchanov ()
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Emmanuel Lépinette: Paris-Dauphine University
Ilya Molchanov: University of Bern

Finance and Stochastics, 2021, vol. 25, issue 1, No 5, 132 pages

Abstract: 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.

Keywords: Acceptance set; Risk arbitrage; Risk measure; Superhedging; Good deal; Solvency set; Random set; Transaction costs; 91G20; 60D05; 60G42 (search for similar items in EconPapers)
JEL-codes: G11 G13 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00780-020-00434-3

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