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Kusuoka (Ann. Appl. Probab. 5:198–221, 1995) showed how to obtain non-trivial scaling limits of superreplication prices in discrete-time models of a single risky asset which is traded at properly scaled proportional transaction costs. This article extends the result to a multivariate setup where the investor can trade in several risky assets. The (G)-expectation describing the limiting price involves models with a volatility range around the frictionless scaling limit that depends not only on the transaction costs coefficients, but also on the chosen complete discrete-time reference model.

The scaling limit of superreplication prices with small transaction costs in the multivariate case