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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we present extensions of the exact simulation algorithmintroduced by Beskos et al. (2006). First, a modification in the order in whichthe simulation is done accelerates the algorithm. In addition, we propose atruncated version of the modified algorithm. We obtain a control of the bias ofthis last version, exponentially small in function of the truncation parameter.Then, we extend it to more general drift functions. Our main result is anunbiased algorithm to approximate the two first derivatives with respect to theinitial condition \(x\) of quantities with the form \(\mathbb{E}\Psi(X_T^x)\).We describe it in details in dimension 1 and also discuss its multi-dimensionalextensions for the evaluation of \(\mathbb{E}\Psi(X_T^x)\). Finally, we applythe algorithm to the CIR process and perform numerical tests to compare it withclassical approximation procedures.

An unbiased Monte Carlo estimator for derivatives. Application to CIR