Monte Carlo methods are a very general and useful approach for the estimation of
expectations arising from stochastic simulation. However, they can be computationally …

Many stochastic differential equations (SDEs) in the literature have a superlinearly growing
nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the …

We are interested in strong approximations of one-dimensional SDEs which have non-
Lipschitz coefficients and which take values in a domain. Under a set of general …

We develop a perturbation theory for stochastic differential equations (SDEs) by which we
mean both stochastic ordinary differential equations (SODEs) and stochastic partial …

In this book, we study stochastic volatility models and methods of pricing, hedging, and
estimation. Among models, we will study models with heavy tails and long memory or long …

We study the convergence of a drift implicit scheme for one-dimensional SDEs that was
considered by Alfonsi (2005) for the Cox–Ingersoll–Ross (CIR) process. Under general …

In this paper, we introduce a new simple approach to developing and establishing the
convergence of splitting methods for a large class of stochastic differential equations (SDEs) …

The celebrated Hörmander condition is a sufficient (and nearly necessary) condition for a
second-order linear Kolmogorov partial differential equation (PDE) with smooth coefficients …

The development of affine processes in modelling has shadowed the expansion of financial
mathematics ever since the pioneering works of Black and Scholes [20] and Merton [106] in …

We consider the approximation of one-dimensional stochastic differential equations (SDEs)
with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler …