Research on Constrained Wiener Processes and Their Financial Applications
For the pricing of so-called exotic options, which have many financial applications, the extremes of the Wiener processes are important. For one dimensional Wiener processes, the probability densities of such extremes are well recognised. For multidimensional Wiener processes, with multiple extremes, we use simple methods to extract analytical expressions for the densities. These take the form of series expansions of Gaussian densities (possibly infinite). This is achieved using the characterization of the Wienerprocess by heatequation, a well-known mathematical physics relation.
Monash University, Melbourne, Australia.
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