Stochastic Calculus of Variations in Mathematical Finance

By Paul Malliavin, Anton Thalmaier. 2005

220 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/ec3e5379119a676c126353c92f4a2953d76890f6

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Citations in the corpus

A Fourier transform method for nonparametric estimation of multivariate volatility (2009, background): “For instance, this feature is essential when a stochastic derivation of volatility along the time evolution is performed as in contingent claim pricing-hedging (see [11, 35]), or when we study the geometry of the Heath–Jarrow–Morton interest rates dynamics given the observation of a single market tr”
On Malliavin's differentiability of BSDEs with time delayed generators driven by Brownian motions and Poisson random measures (2010, methodology): “More generally, it has been established as a key tool in the numerics of control theory and mathematical finance, for instance to enhance the convergence speed of discretization schemes for solutions of BSDE, see [11], [18].”
NONPARAMETRIC ESTIMATION OF THE DIFFUSION COEFFICIENT OF STOCHASTIC VOLATILITY MODELS (2008, unknown): “@ak~s 2 !cos~kt ! bk~s 2 !sin~kt !# , (6.3) where wF is the Fejer kernel ~Priestley, 1979; Malliavin and Thalmaier, 2005!, defined as wF ~x! sin2~x! x 2 , (6.4) and wF~0!”
Stochastic Analysis in Discrete and Continuous Settings: With Normal Martingales (2009, unknown): “[53], [65], [67], [76], [87], [88], [96], [132], [138], [147], [150], [151].”
Absolute continuity and convergence of densities for random vectors on Wiener chaos (2012, methodology): “The method is based on the representation of the density of a Wiener functional using the Poisson kernel obtained by Malliavin and Thalmaier in [9], and it has been further developed by Bally and Caramellino in the works [1] and [2].”