Computing Functionals of Multidimensional Diffusions via Monte Carlo Methods

摘要

We discuss suitable classes of diffusion processes, for which functionalsrelevant to finance can be computed via Monte Carlo methods. In particular, weconstruct exact simulation schemes for processes from this class. However,should the finance problem under consideration require e.g. continuousmonitoring of the processes, the simulation algorithm can easily be embedded ina multilevel Monte Carlo scheme. We choose to introduce the finance problemsunder the benchmark approach, and find that this approach allows us to exploitconveniently the analytical tractability of these diffusion processes.