In financial and actuarial modeling and other areas of application, stochastic differential
equations with jumps have been employed to describe the dynamics of various state …

During the seven years that elapsed between the first and second editions of the present
book, considerable progress was achieved in the area of financial modelling and pricing of …

Recently, there have been conceptually new developments in Monte Carlo methods through
the introduction of new MCMC and sequential Monte Carlo (SMC) algorithms which are …

Suppose a new deck of cards is shuffled. Then as the number of shuffles grows, the
distribution of the deck becomes closer and closer to uniform over the set of permutations of …

Generating sample paths of stochastic differential equations (SDE) using the Monte Carlo
method finds wide applications in financial engineering. Discretization is a popular …

This paper develops a method for the exact simulation of a skeleton, a hitting time, and other
functionals of a one-dimensional jump diffusion with state-dependent drift, volatility, jump …

This paper introduces a framework for simulating finite dimensional representations of
(jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in …

We introduce a variational theory for processes adapted to the multidimensional Brownian
motion filtration that provides a differential structure allowing to describe infinitesimal …

We develop exact random variate generators for several distributions related to the Jacobi
theta function. These include the distributions of the maximum of a Brownian bridge, a …

This paper introduces a class of Monte Carlo algorithms which are based upon simulating a
Markov process whose quasi-stationary distribution coincides with the distribution of interest …