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Sonia Fourati

Publications and source records attributed to Sonia Fourati.

5 recordsLinked to original sources
arXiv2016

On some analytical properties of stable densities

L.Bondesson [1] conjectured that the density of a positive $α$-stable distribution is hyperbolically completely monotone (HCM in short) if and only if $α$ $\le$ 1/2. This was proved recently by P. Bosch and Th. Simon, who also conjectured a strengthened version of this result. We disprove this conjecture as well as a correlated conjecture of Bondesson, while giving a short new proof of the initial conjecture, as a direct consequence of a new algebraic property of HCM and Generalized Gamma convolution densities (GGC in short) which we establish.

math.PR↗
arXiv2010

Explicit solutions for the exit problem for a class of Lévy processes. Applications to the pricing of double barrier options

Lewis and Mordecki have computed the Wiener-Hopf factorization of a Lévy process whose restriction on $]0,+\infty[$ of their Lévy measure has a rational Laplace transform. That allows to compute the distribution of $(X_t,\inf_{0\leq s\leq t}X_s)$. For the same class of Lévy processes, we compute the distribution of $ (X_t,\inf_{0\leq s\leq t}X_s,\sup_{0\leq s\leq t} X_s)$ and also the behavior of this triple at certain stopping time, like the first exit time of an interval containing the origin. Some applications to the pricing of double barrier options with or without rebate are evocated.

math.PR↗
arXiv2007

Fluctuations of Levy processes and scattering theory

We establish a connection between the scattering inverse problem and the determination of the distribution of the position of the Levy process at the exit time of a bounded interval in term of its Levy exponent.

math.PR↗
arXiv2005

Krein's Theory applied to fluctuations of Lévy processes

We give an interpretation of the bilateral exit problem for Lévy processes via the study of an elementary Markov chain. We exhibit a strong connection between this problem and Krein's theory on strings. For instance, for symmetric Lévy processes with bounded variations, the Lévy exponent is the correspondant spectral density and the Wiener-Hopf factorization turns out to be a version of Krein's entropy formula.

math.PR↗