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Differential geometry. Global analysis --- Geometry, Differential --- Calculus of variations --- 514.76 --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- Geometry of differentiable manifolds and of their submanifolds --- 514.76 Geometry of differentiable manifolds and of their submanifolds --- Lie groups --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Differential geometry --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Manifolds (Mathematics) --- Calculus of variations. --- Variétés (mathématiques) --- Calcul des variations. --- Geometry, Differential. --- Géometrie différentielle --- Lie, Groupes de --- Calcul des variations --- Géometrie différentielle --- Variétés (mathématiques) --- Variétés différentiables

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Malliavin calculus provides an infinite-dimensional differential calculus in the context of continuous paths stochastic processes. The calculus includes formulae of integration by parts and Sobolev spaces of differentiable functions defined on a probability space. This new book, demonstrating the relevance of Malliavin calculus for Mathematical Finance, starts with an exposition from scratch of this theory. Greeks (price sensitivities) are reinterpreted in terms of Malliavin calculus. Integration by parts formulae provide stable Monte Carlo schemes for numerical valuation of digital options. Finite-dimensional projections of infinite-dimensional Sobolev spaces lead to Monte Carlo computations of conditional expectations useful for computing American options. The discretization error of the Euler scheme for a stochastic differential equation is expressed as a generalized Watanabe distribution on the Wiener space. Insider information is expressed as an infinite-dimensional drift. The last chapter gives an introduction to the same objects in the context of jump processes where incomplete markets appear.

Finance --- Stochastic processes. --- Finances --- Processus stochastiques --- Mathematical models. --- Modèles mathématiques --- Finance. --- Finance - Mathematical models. --- Stochastic processes --- Mathematics --- Business & Economics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Finance - General --- Economic Theory --- Mathematical models --- Modèles mathématiques --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Random processes --- Mathematical analysis. --- Analysis (Mathematics). --- Economics, Mathematical. --- Public finance. --- Economics. --- Public Economics. --- Quantitative Finance. --- Analysis. --- Cameralistics --- Public finance --- Currency question --- Economics --- Mathematical economics --- Econometrics --- 517.1 Mathematical analysis --- Mathematical analysis --- Methodology --- Probabilities --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Funding --- Funds --- Public finances --- Economics, Mathematical . --- Finance, Public. --- Social sciences --- Mathematics in Business, Economics and Finance. --- Mathematics.