White Noise Generalization of the Clark–Ocone Formula under Change of Measure
Abstract
This paper develops a white noise generalization of the Clark–Ocone formula under a change of probability measure, combining Gaussian white noise analysis with Malliavin calculus. The study extends the classical representation of stochastic processes by deriving results for square-integrable random variables within a generalized functional framework.
The theoretical contribution includes the formulation of the Clark–Ocone representation under equivalent probability measures and the introduction of related Malliavin derivative structures. The paper also demonstrates practical applications in finance, particularly in constructing replicating portfolios for contingent claims such as digital options.
The results provide a rigorous mathematical foundation for extending stochastic calculus tools to more complex probabilistic settings and financial modeling contexts.
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