On discrete time hedging in d-dimensional option pricing models
Abstract
We study the approximation of certain stochastic integrals with respect to a d-dimensional diffusion by corresponding stochastic integrals with piece-wise constant integrands. In finance this corresponds to replacing a continuously adjusted portfolio by discretely adjusted one. The approximation error is measured with respect to L2 and it is shown that under certain assumptions the approximation rate is n-1/2 when one optimizes over deterministic but not necessarily equidistant time-nets.
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