Stochastic Calculus of Variations in Mathematical Finance

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Malliavin calculus serves as an infinite-dimensional differential calculus applicable to continuous path stochastic processes, featuring integration by parts and Sobolev spaces. This book starts with foundational concepts and highlights its significance in Mathematical Finance, particularly in interpreting Greeks and developing stable Monte Carlo schemes for digital options valuation. It explores finite-dimensional projections for conditional expectations in American options and addresses discretization errors in stochastic differential equations. The final chapter introduces jump processes and incomplete markets.