Chaotic and predictable representation for L'evy Processes

By David Nualart, Wim Schoutens. 2000

292 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/e4071bebedce01cc97ddf60608c0fa21a0c88d24

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Citations in the corpus

BSDE associated with Lévy processes and application to PDIE (2003, methodology): “It was shown in Nualart and Schoutens [6] that the coefficients ci,k correspond to the orthonormalization of the polynomials 1, x, x(2), .”
Martingale Representation of Functionals of Lévy Processes (2004, background): “For general F ∈ L2 T P this implies that the rest term , given by (13), must be orthogonal to all variables of the form (6).”
Askey--Wilson polynomials, quadratic harnesses and martingales (2008, background): “-Wilson polynomials are orthogonal martingale polynomials for these processes. 1. Introduction Orthogonal martingale polynomials for stochastic processes have been studied by a number of authors, see [5, 13, 18, 22, 24, 25, 27, 28]. Orthogonal martingale polynomials play also a prominent role in non”
Appell polynomials and their relatives (2003, background): “Free and even q-analogs of Corollary 4 hold, derived from appropriate modifications of Corollary 2. These properties are related to the “generalized chaos decomposition property” of [ 37 ].”
Explicit Representation of the Minimal Variance Portfolio in Markets Driven by Lévy Processes (2003, methodology): “Then there are constants M(i ) > 0 such that [γ (i ), γ (i )]t = M(i )t (cf. Nualart and Schoutens 2000, Sec.”
Malliavin Monte Carlo Greeks for jump diffusions (2006, background): “More recently, Nualart and Schoutens (2000) developed a theory of chaos expansions for functionals of Lévy processes when the Lévy measure satisfies an exponential moment condition.”
Polynomials of Meixner's type in infinite dimensions-Jacobi fields and orthogonality measures (2002, result): “In a forthcoming paper, we will study a connection between the extended Fock space decomposition of L2(D′; � �) obtained in this paper and the chaotic decomposition of this space in the case X = R as in [ 27 ].”
REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A LÉVY PROCESS (2008, methodology): “Recently, Nualart and Schoutens [16] gave a martingale representation theorem associated with a Lévy process.”