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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...

Covariance structure of wide-sense Markov processes of order k ≥ 1

Arkadiusz Kasprzyk, Władysław Szczotka (2006)

Applicationes Mathematicae

A notion of a wide-sense Markov process X t of order k ≥ 1, X t W M ( k ) , is introduced as a direct generalization of Doob’s notion of wide-sense Markov process (of order k=1 in our terminology). A base for investigation of the covariance structure of X t is the k-dimensional process x t = ( X t - k + 1 , . . . , X t ) . The covariance structure of X t W M ( k ) is considered in the general case and in the periodic case. In the general case it is shown that X t W M ( k ) iff x t is a k-dimensional WM(1) process and iff the covariance function of x t has the triangular property....

Cumulative processes in basketball games

I. Kopocińska, B. Kopociński (2006)

Applicationes Mathematicae

We assume that the current score of a basketball game can be modeled by a bivariate cumulative process based on some marked renewal process. The basic element of a game is a cycle, which is concluded whenever a team scores. This paper deals with the joint probability distribution function of this cumulative process, the process describing the host's advantage and its expected value. The practical usefulness of the model is demonstrated by analyzing the effect of small modifications of the model...

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