Central limit theorems for multilevel Monte Carlo methods

Multilevel Monte Carlo for Asian options and limit theorems

The purpose of this paper is to study the problem of pricing Asian options using the multilevel Monte Carlo method recently introduced by Giles [8] and to prove a central limit theorem of Lindeberg Feller type for the obtained algorithm. Indeed, the implementation of such a method requires first a discretization of the integral of the payoff process. To do so, we use two well-known second order...

Multilevel Monte Carlo Methods

We study Monte Carlo approximations to high dimensional parameter dependent integrals. We survey the multilevel variance reduction technique introduced by the author in [4] and present extensions and new developments of it. The tools needed for the convergence analysis of vector-valued Monte Carlo methods are discussed, as well. Applications to stochastic solution of integral equations are give...

Massively parallel Multilevel Monte Carlo methods

Multilevel Monte Carlo methods and uncertainty quantification

Attention is drawn to the fact that copyright of this thesis rests with its author. This copy of the thesis has been supplied on the condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without the prior written consent of the author. This thesis may be ...

Limit theorems for weighted samples with applications to Sequential Monte Carlo Methods

In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics (see for instance Doucet et al. (2001), Liu (2001), Künsch (2001)). These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted population of particles. These particles and weights are generated recursively according to ele...