Adaptive Monte Carlo algorithm of killed diffusion

Kyoung-Sook Moon

Abstract

I will present an adaptive algorithm for weak approximations of stochastic differential equations by Monte Carlo Euler method. The goal is to compute expected values of functions of the solution depending on the first exit time from a given domain. In particular, I will explain why killed diffusions are good examples where adaptive methods are very useful.

The algorithm is based on the error expansion with a posteriori leading order term introduced in [A. Szepessy, R. Tempone and G. Zouraris, Comm. Pure and Appl. Math., 54, 1169-1214, 2001] with almost optimal convergence rate proven in [K-S. Moon, A. Szepessy, R. Tempone and G. Zouraris, preprint, http://www.nada.kth.se/~szepessy/sode.ps].

Finally, I will show numerical results from computations of barrier options in financial mathematics.