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TY  - BOOK
ID  - 5406993
TI  - Stochastic calculus of variations in mathematical finance
AU  - Malliavin, Paul
AU  - Thalmaier, Anton.
PY  - 2006
SN  - 3540434313 3642077838 9786610462568 1280462566 3540307990
PB  - Berlin ; New York : Springer,
DB  - UniCat
KW  - Finance
KW  - Stochastic processes.
KW  - Finances
KW  - Processus stochastiques
KW  - Mathematical models.
KW  - Modèles mathématiques
KW  - Finance.
KW  - Finance - Mathematical models.
KW  - Stochastic processes
KW  - Mathematics
KW  - Business & Economics
KW  - Physical Sciences & Mathematics
KW  - Mathematical Statistics
KW  - Finance - General
KW  - Economic Theory
KW  - Mathematical models
KW  - Modèles mathématiques
KW  - EPUB-LIV-FT LIVMATHE SPRINGER-B
KW  - Random processes
KW  - Mathematical analysis.
KW  - Analysis (Mathematics).
KW  - Economics, Mathematical.
KW  - Public finance.
KW  - Economics.
KW  - Public Economics.
KW  - Quantitative Finance.
KW  - Analysis.
KW  - Cameralistics
KW  - Public finance
KW  - Currency question
KW  - Economics
KW  - Mathematical economics
KW  - Econometrics
KW  - 517.1 Mathematical analysis
KW  - Mathematical analysis
KW  - Methodology
KW  - Probabilities
KW  - Global analysis (Mathematics).
KW  - Analysis, Global (Mathematics)
KW  - Differential topology
KW  - Functions of complex variables
KW  - Geometry, Algebraic
KW  - Funding
KW  - Funds
KW  - Public finances
KW  - Economics, Mathematical .
KW  - Finance, Public.
KW  - Social sciences
KW  - Mathematics in Business, Economics and Finance.
KW  - Mathematics.
UR  - https://www.unicat.be/uniCat?func=search&query=sysid:5406993
AB  - 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.
ER  -