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Variational representations for continuous time processes

Amarjit Budhiraja, Paul Dupuis, Vasileios Maroulas (2011)

Annales de l'I.H.P. Probabilités et statistiques

A variational formula for positive functionals of a Poisson random measure and brownian motion is proved. The formula is based on the relative entropy representation for exponential integrals, and can be used to prove large deviation type estimates. A general large deviation result is proved, and illustrated with an example.

Vervaat et Lévy

Sonia Fourati (2005)

Annales de l'I.H.P. Probabilités et statistiques

Viscosity solutions and American option pricing in a stochastic volatility model of the Ornstein-Uhlenbeck type.

Roch, Alexandre F. (2010)

Journal of Probability and Statistics

Wavelet method for option pricing under the two-asset Merton jump-diffusion model

Černá, Dana (2021)

Programs and Algorithms of Numerical Mathematics

This paper examines the pricing of two-asset European options under the Merton model represented by a nonstationary integro-differential equation with two state variables. For its numerical solution, the wavelet-Galerkin method combined with the Crank-Nicolson scheme is used. A drawback of most classical methods is the full structure of discretization matrices. In comparison, the wavelet method enables the approximation of discretization matrices with sparse matrices. Sparsity is essential for the...

α-stable random walk has massive thorns

Alexander Bendikov, Wojciech Cygan (2015)

Colloquium Mathematicae

We introduce and study a class of random walks defined on the integer lattice $ℤ^{d}$ -a discrete space and time counterpart of the symmetric α-stable process in $ℝ^{d}$ . When 0 < α <2 any coordinate axis in $ℤ^{d}$ , d ≥ 3, is a non-massive set whereas any cone is massive. We provide a necessary and sufficient condition for a thorn to be a massive set.