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 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...

Using the Malliavin calculus on Poisson space we compute the probability density of risk reserve processes and the sensitivities of probabilities of ruin at a given date for an insurance portfolio under interest force. We follow a method initiated in Fournie et al. Finance and Stochastics 3(4)...

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

"It is a fairly complete introduction accessible to advanced undergraduates; Also covers more advanced aspects of interest rate modeling; Includes many graphs and code illustrating the modeling of interest rates; Each chapter is accompanied with exercises and their complete solutions."