A central limit theorem and improved error bounds for a hybrid-Monte Carlo sequence with applications in computational finance
Résumé
In problems of moderate dimensions, the quasi-Monte Carlo method usually provides better estimates than the Monte Carlo method. However, as the dimension of the problem increases, the advantages of the quasi-Monte Carlo method diminish quickly. A remedy for this problem is to use hybrid sequences; sequences that combine pseudorandom and low-discrepancy vectors. In this paper we discuss a particular hybrid sequence called the mixed sequence. We will provide improved discrepancy bounds for this sequence and prove a central limit theorem for the corresponding estimator. We will also provide numerical results that compare the mixed sequence with the Monte Carlo and randomized quasi-Monte Carlo methods.