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Constrained Wiener Processes and Their Financial Applications

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Document pages: 20 pages

Abstract: The extrema of Wiener processes are relevant to the pricing of so-called exoticoptions, which have many financial applications. The probability densitiesof such extrema are well known for one dimensional Wiener processes. Weemploy elementary methods to derive analytical expressions for the densitiesfor multidimensional Wiener processes, with multiple extrema. These takethe form of (possibly infinite) series expansions of Gaussian densities. This isundertaken using the characterization of the Wiener process by the heat equation,a well known connection in mathematical physics.

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