Monte Carlo and Quasi-Monte Carlo Conference edition:8 location:HEC, Université de Montréal, Canada date:6-11 July 2008
Derivative pricing problems can often be nicely formulated as high dimensional integrals and as such quasi-Monte Carlo
rules can be applied to calculate their fair price.
For some of these high dimensional integrals it is known that the effective dimension of the problem is actually quite
low, say two instead of hundreds.
This fact alone is already an important stimulant to use a quasi-Monte Carlo method over a standard Monte Carlo one.
Additionally, for some low to moderate dimensional integrals it pays off to apply adaptive methods, however if the dim
ension is too high one quickly runs into problems.
Two well known adaptive methods, MISER and VEGAS, have already been adapted to be used with quasi-Monte Carlo integrat
ion, see (Schürer, 2002).
The problems we consider in this talk however do not fall into the category of being moderate dimensional.
A natural idea now is to combine the concepts of low effective dimension and classical adaptive algorithms for solving
high dimensional problems.
Depending on the effective low dimensionality the adaptive strategy could range from classical quadrature or cubature
to adaptive QMC.
In this talk we will explore the possibilities of these combinations.
This talk explores further ideas on adaptive QMC strategies from joint work with Ben Waterhouse (Nuyens & Waterhouse, working paper).