English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In Costantini (1999) it was shown how the simplest variance reduction technique, the so called method of antithetic random numbers (ARN), can be applied to the main discretization schemes both for unrestricted diffusion processes and for diffusion processes with normal reflection in an orthant (these results are recalled in Section 2 and 4, respectively). While most variance reduction methods require ad hoc mathematical work for each specific model, for the ARN method one can state simple conditions to be verified. Moreover the ARN method is extremely simple to implement and can be used for all monotone functionals of the paths. For the ARN method to work, the coefficients of the stochastic differential equations must satisfy certain monotonicity assumptions, which are, in principle, somewhat restrictive, at least in dimension bigger than one. However the goal of this paper is precisely to show that there are significant examples in finance (Section 3) and in queueing theory (Section 5) to which the ARN method applies. The numerical results in Section 3 exhibit a considerable variance reduction. The class of examples of Section 5 is a class of multidimensional Brownian motions with oblique reflection in an orthant. In Section 4, it is proved that the ARN method applies to the Euler-oblique projection scheme in an orthant with directions of reflection pointing toward the corner. Finally, the following terminology and notation will be used throughout the paper: Increasing, decreasing, positive, negative will always be meant in the broad sense. Given x,y G R, the notation x < y

A SIMPLE VARIANCE REDUCTION METHOD WITH APPLICATIONS TO FINANCE AND QUEUEING THEORY