This paper deals with an extension of the concept of correlated strategies to Markov stopping games. The Nash equilibrium approach to solving nonzero-sum stopping games may give multiple solutions. An arbitrator can suggest to each player the decision to be applied at each stage based on a joint distribution over the players' decisions. This is a form of equilibrium selection. Examples of correlated equilibria in nonzero-sum games related to the staff selection competition in the case of two departments...

This paper is a corrigendum to paper Toldo, ESAIM, P&S10 (2006) 141–163 where we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely finite random terminal time.

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...

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...

A toute mesure $c$ positive sur ${ℝ}_{+}$ telle que ${\int }_0^{\infty }(x\wedge x^2)c\left(dx\right)\<\infty$, 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, $H\ge 0$, et pour tout $\lambda \ge 0,E\left(e^{\lambda X}\right)·E\left(e^{-\frac{{\lambda }^2}{2}H}\right)=1$. Plus généralement, à une mesure $c$ positive sur ${ℝ}_{+}$ telle que ${\int }_0^{\infty }{e}^{-\alpha x}{x}^{2}c\left(dx\right)\<\infty$ pour tout $\alpha \>{\alpha }_0$, 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...

A notion of a wide-sense Markov process $X_t$ of order k ≥ 1, $X_t\sim WM\left(k\right)$, 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 $X_t\sim WM\left(k\right)$ is considered in the general case and in the periodic case. In the general case it is shown that $X_t\sim WM\left(k\right)$ iff $x_t$ is a k-dimensional WM(1) process and iff the covariance function of $x_t$ has the triangular property....

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...