The scaling limit of superreplication prices with small transaction costs in the multivariate case. (English) Zbl 1378.91132
Authors’ abstract: S. Kusuoka [Ann. Appl. Probab. 5, No. 1, 198–221 (1995; Zbl 0834.90049)] 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.
Reviewer: Pedro A. Morettin (São Paulo)
MSC:
| 91G99 | Actuarial science and mathematical finance |
| 91B25 | Asset pricing models (MSC2010) |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 60F05 | Central limit and other weak theorems |
| 60F17 | Functional limit theorems; invariance principles |
| 91G10 | Portfolio theory |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
Citations:
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