d - dimensional option pricing models
نویسنده
چکیده
We study the approximation of certain stochastic integrals with respect to a d-dimensional diffusion by corresponding stochastic integrals with piece-wise constant inte-grands i.e. an approximation of the form d k=1 T 0 N k s dX k s ≈ d k=1 n i=1 N k t i−1 (X k t i − X k t i−1). 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 0 = t 0 ≤ t 1 ≤ · · · ≤ t n = T .
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