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This monograph discusses the existence and regularity properties of local times associated to a continuous semimartingale, as well as excursion theory for Brownian paths.
Although one might argue whether this golden age is really foregone, and discuss the "height" of the technology involved, this quotation is closely related to the main motivations of Part II: this technology, which includes stochastic calculus for general discontinuous semi-martingales, enlargement of filtrations, .
Stochastic processes of common use in mathematical finance are presented in this book, which interlaces financial concepts and instruments such as arbitrage opportunities, option pricing and default risk with Brownian motion and Levy and diffusion processes.
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