We developed a new scheme for computing ”Greeks” of derivatives by an asymptotic expansion approach. In particular, we derived analytical approximation formulae for Deltas and Vegas of plain vanilla and average European call options under general Markovian processes of underlying asset prices. Moreover, we introduced a new variance reduction method of Monte Carlo simulations based on the asympt...

The machine learning model converges slowly and has unstable training since large variance by random using a sample estimate gradient in SGD. To this end, we propose noise reduction method for Stochastic Variance Reduction (SVRG), called N-SVRG, which uses small batches samples instead of all the average calculation, while performing an incremental update gradient. In each round iteration, batc...

We consider the computation of free energy-like quantities for diffusions when resorting to Monte Carlo simulation is necessary, instance in high dimension. Such stochastic computations typically suffer from variance, particular a low noise regime, because expectation dominated by rare trajectories which observable reaches large values. Although importance sampling, or tilting trajectories, now...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 20 August 2020Accepted: 01 September 2021Published online: 05 January 2022Keywordsdecentralized optimization, stochastic nonconvex variance reduction, gradient trackingAMS Subject Headings90C26, 90C15, 93A16Publication DataISSN (print): 1052-6234ISSN (online): 1095-7189Pu...

After a brief description of the essentials Monte Carlo simulation methods and definition efficiency, rationale for variance-reduction techniques is presented. Popular applicable to simulations radiation transport are described motivated. The focus on those that can be used with any code, irrespective strategies track charged particles; they operate by manipulating either number weights transpo...