Preface This text is an introduction to pricing and hedging in discrete and continuous time financial models without friction (i.e. without transaction costs), with an emphasis on the complementarity between analytical and probabilistic methods. Its contents are mostly mathematical, and also aim...

We use a white noise approach to Malliavin calculus to prove the following white noise generalization of the Clark-Haussmann-Ocone formula <p>\[F(\omega)=E[F]+\int_0^TE[D_tF|\F_t]\diamond W(t)dt\] <p>Here E[F] denotes the generalized expectation, $D_tF(\omega)={{dF}\over{d\omega}}$ is the...</p></p>

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...

Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes using their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for...

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...