Journal ArticleDOI
Processes of Meixner type
TLDR
In this paper, the Esscher transforms of mixed Meixner processes are defined and characterized as Markov processes or semimartingales, and Ornstein-Uhlenbeck and self-similar processes of MeixNER type are also described.Abstract:
Canonical form, self-decomposability, and the Esscher transforms of Meixner processes are discussed. Mixed Meixner processes are defined and characterized as Markov processes or semimartingales. Ornstein-Uhlenbeck and selfsimilar processes of Meixner type are also described.read more
Citations
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Book ChapterDOI
Shrink Globally, Act Locally: Sparse Bayesian Regularization and Prediction
TL;DR: In this paper, the classic problem of choosing a prior distribution for a location parameter β = (β1,..., βp) as p grows large is studied.
Journal ArticleDOI
Chaotic and predictable representations for Levy processes
David Nualart,Wim Schoutens +1 more
TL;DR: The only normal martingales which posses the chaotic representation property and the weaker predictable representation property, which are at the same time also Levy processes, are in essence Brownian motion and the compensated Poisson process.
Journal ArticleDOI
Backward stochastic differential equations and Feynman-Kac formula for Levy processes, with applications in finance
David Nualart,Wim Schoutens +1 more
TL;DR: In this paper, the existence and uniqueness of a solution for backward stochastic differential equations driven by a Levy process with moments of all orders is shown. And the results are important from a pure mathematical point of view as well as in the world of finance: an application to Clark-Ocone and Feynman-Kac formulas for Levy processes is presented.
Journal ArticleDOI
Self-decomposability and option pricing
TL;DR: In this article, the authors investigated six different processes in this general class and showed that all six models are capable of adequately synthesizing European option prices across the spectrum of strikes and maturities at a point of time.
Journal ArticleDOI
Local shrinkage rules, Lévy processes and regularized regression
TL;DR: The authors use L´ evy processes to generate joint prior distributions, and therefore penalty functions, for a location parameter b = (b1;:::;;bp) as p grows large.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Journal ArticleDOI
The Variance Gamma (V.G.) Model for Share Market Returns
Dilip B. Madan,Eugene Seneta +1 more
TL;DR: In this paper, a new stochastic process, termed the variance gamma process, is proposed as a model for the uncertainty underlying security prices, which is normal conditional on a variance, distributed as a gamma variate.
Journal ArticleDOI
Processes of normal inverse Gaussian type
TL;DR: A number of stochastic processes with normal inverse Gaussian marginals and various types of dependence structures are discussed, including Ornstein-Uhlenbeck type processes, superpositions of such processes and Stochastic volatility models in one and more dimensions.
Journal ArticleDOI
Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling
TL;DR: In this article, the potential of the normal inverse Gaussian distribution and the Levy process for modeling and analysing statistical data, with particular reference to extensive sets of observations from turbulence and from finance, is discussed.