Quasi-Monte Carlo methods with applications in finance

Monte Carlo, Quasi-Monte Carlo, Variance reduction, Effective dimension, Discrepancy, Hilbert spaces, 65C05, 68U20, 91B28, C15, C63,

Scrambled polynomial lattice rules for infinite-dimensional integration

In the random case setting, scrambled polynomial lattice rules, as discussed in Baldeaux and Dick (Numer. Math. 119:271-297,2011), enjoy more favorable strong tractability properties than crambled digital nets. This short note discusses the application of scrambled polynomial lattice rules to infinitedimensional integration. In Hickemell et al. (J Complex 26:229-254, 2010), infinitedimensional integration in the random case setting was examined in detail, and results based on scrambled digital nets were presented. Exploiting these improved strong tractability properties of scrambled polynomial lattice rules and making use of the analysis presented.in Hickemell et al (J Complex 26:229-254, 2010), we improve on the results that were achieved using scrambled digital nets

When does quasi-random work?

[10, 22] presented various ways for introducing quasi-random numbers or derandomization in evolution strategies, with in some cases some spectacular claims on the fact that the proposed technique was always and for all criteria better than standard mutations. We here focus on the quasi-random trick and see to which extent this technique is efficient, by an in-depth analysis including convergence rates, local minima, plateaus, nonasymptotic behavior and noise. We conclude to the very stable, efficient and straightforward applicability of quasi-random numbers in continuous evolutionary algorithms