On quantitative approximation of stochastic integrals with respect to the geometric Brownian motion

We approximate stochastic integrals with respect to the geometric Brownian motion by stochastic integrals over discretized integrands, where deterministic, but not necessarily equidistant, time nets are used. This corresponds to the approximation of a continuously adjusted portfolio by a discretely adjusted one. We compute the approximation orders of European Options in the Black Scholes model with respect to L_2 and the approximation order of the standard European-Call and Put Option with respect to an appropriate BMO space, which gives information about the cost process of the discretely adjusted portfolio. (author's abstract) ; Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Stefan Geiss

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