Risk arbitrage and hedging to acceptability under transaction costs
Lépinette, Emmanuel; Molchanov, Ilya (2021), Risk arbitrage and hedging to acceptability under transaction costs, Finance and Stochastics, 25, p. 101–132. 10.1007/s00780-020-00434-3
TypeArticle accepté pour publication ou publié
Journal nameFinance and Stochastics
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Institute of Mathematical Statistics and Actuarial Science [Bern] [IMSV]
Abstract (EN)The classical discrete time model of transaction costs relies on the assumption that the increments of the feasible portfolio process belong to the solvency set at each step. We extend this setting by assuming that any such increment belongs to the sum of an element of the solvency set and the family of 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. If the acceptance sets consist of non-negative random vectors, that is the underlying dynamic risk measure is the conditional essential infimum, we extend many classical no arbitrage conditions in markets with transaction costs and provide their natural geometric interpretation. The mathematical technique relies on results for unbounded and possibly non-closed random sets in the Euclidean space.
Subjects / Keywordsacceptance set; risk arbitrage; risk measure; superhedging; solvency set; random set; transaction costs
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