On discrete time hedging in d-dimensional option pricing models

Mika Hujo

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On discrete time hedging in d-dimensional option pricing models

Mika Hujo

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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 $L^2$ 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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Mika Hujo. 2007-03-16. On discrete time hedging in d-dimensional option pricing models. https://arxiv.org/abs/math/0703481

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