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.
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 for 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 the assets lead to a decrease of superhedging prices and the no arbitrage conditions become stronger . The mathematical technique relies on results for unbounded and possibly non-closed random sets in Euclidean space.
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the increments of the
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by assuming that any such increment belongs
in two directions, allowing for convex transaction costs and assuming that increments of the portfolio process belong
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an element of the
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the family of
a family of multivariate
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risk
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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
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 the assets lead to a decrease of superhedging prices and the
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in markets with transaction costs and provide their natural geometric interpretation
become stronger
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