We consider the Euler approximation of stochastic differential equations (SDEs) driven by Lévy processes in the case where we cannot simulate the increments of the driving process exactly. In some cases, where the driving process Y is a subordinated stable process, i.e., Y=Z(V) with V a...

We study simulated annealing algorithms to maximise a function [psi] on a subset of . In classical simulated annealing, given a current state [theta]n in stage n of the algorithm, the probability to accept a proposed state z at which [psi] is smaller, is exp(-[beta]n+1([psi](z)-[psi]([theta]n))...

The Euler scheme is a well-known method of approximation of solutions of stochastic differential equations (SDEs). A lot of results are now available concerning the precision of this approximation in case of equations driven by a drift and a Brownian motion. More recently, people got interested...

Building on the work of Schweizer (1995) and Cern and Kallseny (2007), we present discrete time formulas minimizing the mean square hedging error for multidimensional assets. In particular, we give explicit formulas when a regime-switching random walk or a GARCH-type process is utilized to model...

While statisticians are well-accustomed to performing exploratory analysis in the modeling stage of an analysis, the notion of conducting preliminary general-purpose exploratory analysis in the Monte Carlo stage (or more generally, the model-fitting stage) of an analysis is an area that we feel...

We present a multivariate central limit theorem for a general class of interacting Markov chain Monte Carlo algorithms used to solve nonlinear measure-valued equations. These algorithms generate stochastic processes which belong to the class of nonlinear Markov chains interacting with their...

The aim of this article is to give a general introduction to the theory of interacting particle methods, and an overview of its applications to computational finance. We survey the main techniques and results on interacting particle systems and explain how they can be applied to the numerical...