We derive necessary and sufficient conditions for the supermodular ordering of certain triangular arrays of Poisson random variables, based on the componentwise ordering of their covariance matrices. Applications are proposed for markets driven by jump–diffusion processes, using sums of...

Using finite difference operators, we define a notion of boundary and surface measure for configuration sets under Poisson measures. A Margulis-Russo type identity and a co-area formula are stated with applications to bounds on the probabilities of monotone sets of configurations and on related...

We obtain lower and upper bounds on option prices in one-dimensional jump-diffusion markets with point process components. Our proofs rely in general on the classical Kolmogorov equation argument and on the propagation of convexity property for Markov semigroups, but the bounds on intensities...

We state an abstract version of covariance identities and inequalities for normal martingales, which uses any gradient operator that satisfies a Clark formula. This extends and makes more precise some results of Houdré and Pérez-Abreu (Ann. Probab. 23 (1995)), with simplified proofs.

We compute the Wiener-Poisson expansion of square-integrable functionals of a finite number of Poisson jump times in series of multiple Poisson stochastic integrals.

Using the Malliavin calculus on Poisson space we compute Greeks in a market driven by a discontinuous process with Poisson jump times and random jump sizes, following a method initiated on the Wiener space in [5]. European options do not satisfy the regularity conditions required in our...

Using the Malliavin calculus in time inhomogeneous jump-diffusion models, we obtain an expression for the sensitivity Theta of an option price (with respect to maturity) as the expectation of the option payoff multiplied by a stochastic weight. This expression is used to design efficient...