Pathwise Construction of Stochastic Integrals

Abstract

We propose a method to construct the stochastic integral simultaneously under a non-dominated family of probability measures. Path-by-path, and without referring to a probability measure, we construct a sequence of Lebesgue-Stieltjes integrals whose medial limit coincides with the usual stochastic integral under essentially any probability measure such that the integrator is a semimartingale. This method applies to any predictable integrand.

9 pages

References in corpus (1)

• A theoretical framework for the pricing of contingent claims in the presence of model uncertainty

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