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Cost-efficiency in multivariate Lévy models

Ludger Rüschendorf, Viktor Wolf (2015)

Dependence Modeling

In this paper we determine lowest cost strategies for given payoff distributions called cost-efficient strategies in multivariate exponential Lévy models where the pricing is based on the multivariate Esscher martingale measure. This multivariate framework allows to deal with dependent price processes as arising in typical applications. Dependence of the components of the Lévy Process implies an influence even on the pricing of efficient versions of univariate payoffs.We state various relevant existence...

Counting walks in a quadrant: a unified approach via boundary value problems

Kilian Raschel (2012)

Journal of the European Mathematical Society

The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this yields for the first time an explicit expression of the counting generating function. Moreover, the nature of the integrand of the integral formulations is shown to be directly dependent on the finiteness of a naturally attached group of birational transformations...

Couples de Wald indéfiniment divisibles. Exemples liés à la fonction gamma d'Euler et à la fonction zeta de Riemann

Bernard Roynette, Marc Yor (2005)

Annales de l’institut Fourier

A toute mesure c positive sur + telle que 0 ( x x 2 ) c ( d x ) < , nous associons un couple de Wald indéfiniment divisible, i.e. un couple de variables aléatoires ( X , H ) tel que X et H sont indéfiniment divisibles, H 0 , et pour tout λ 0 , E ( e λ X ) · E ( e - λ 2 2 H ) = 1 . Plus généralement, à une mesure c positive sur + telle que 0 e - α x x 2 c ( d x ) < pour tout α > α 0 , nous associons une “famille d’Esscher” de couples de Wald indéfiniment divisibles. Nous donnons de nombreux exemples de telles familles d’Esscher. Celles liées à la fonction gamma et à la fonction zeta de Riemann possèdent...

Coupling a branching process to an infinite dimensional epidemic process***

Andrew D. Barbour (2010)

ESAIM: Probability and Statistics

Branching process approximation to the initial stages of an epidemic process has been used since the 1950's as a technique for providing stochastic counterparts to deterministic epidemic threshold theorems. One way of describing the approximation is to construct both branching and epidemic processes on the same probability space, in such a way that their paths coincide for as long as possible. In this paper, it is shown, in the context of a Markovian model of parasitic infection, that coincidence...

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