Titlebook: Séminaire de Probabilités XXXVII; Jacques Azéma,Michel Émery,Marc Yor Book 2003 Springer-Verlag Berlin Heidelberg 2003 Black-Scholes.Brown

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A note on representations of eigenvalues of classical Gaussian matrices,servation due to Johansson in order to derive new representations for the eigenvalues of GUE. For instance, it is possible to recover the celebrated equality in distribution between the maximal eigenvalue of GUE and a last-passage time in some directed Brownian percolation. Similar identities for the other eigenvalues of GUE also appear.

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,On the Derivation of the Black–Scholes Formula, is mathematically justified. In the process, we have to confront a novel free boundary problem for parabolic equations.. Derivative pricing, Black Scholes equation, call option, self financing, hedging portfolio, parabolic equation.

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The Codimension of the Zeros of a Stable Process in Random Scenery,te consequence, we deduce that the Hausdorff dimension of the zeros of the latter process is almost surely equal to (2.).. This solves Conjecture 5.2 of [6], thereby refining a computation of [10].. Random walk in random scenery; stochastic codimension; Hausdorff dimension.. 60K37

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,Deux notions équivalentes d’unicité en loi pour les équations différentielles stochastiques,r all solutions the law of is the same), and a stronger one (all solutions have the same law). These two definitions are shown to be equivalent; more precisely, when the law of is extremal in the set of all laws of solutions, the law of is determined by that of.

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