journal: Monte Carlo Methods and Applications

Impact Factor: 0.6

Zeitschrift

Monte Carlo Methods and Applications

Managing Editor: Karl K. Sabelfeld
Wissenschaftlicher Beirat: Kurt Binder , Nicolas Bouleau , Alexandre J. Chorin , Ivan Dimov , Alain Dubus , Alexander D. Egorov , Sergei M. Ermakov , John H. Halton , Stefan Heinrich , Chi-Ok Hwang , Malvin H. Kalos , Dmitry R. Kolyukhin , D. Lepingle , Yaohang Li , Roman Makarov , Michael Mascagni , Peter Mathe , Harald Niederreiter , Giray Ökten  , Shigeyoshi Ogawa , Eckhard Platen , Brian R. Sawford , Wolfgang Ch. Schmid , John Schoenmakers , Irina A. Shalimova , Ilya M. Sobol , Jerry Spanier , Denis Talay und Wolfgang Wagner

Sprache: Englisch

Erstveröffentlichung: 1. Januar 1995

Erscheinungsweise: 4 Hefte pro Jahr

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Über diese Zeitschrift

Objective
Monte Carlo Methods and Applications is a quarterly published journal that presents original articles on the theory and applications of Monte Carlo and Quasi-Monte Carlo methods. Launched in 1995 the journal covers all stochastic numerics topics with emphasis on the theory of Monte Carlo methods and new applications in all branches of science and technology. Stochastic models in all fields of applied sciences, in particular turbulence, rarefied gas dynamics and nanotechnology, bioscience, medicine, chemical kinetics and combustion, stochastic models in mathematical finance

Topics

Theory of Monte Carlo methods
Quasi-Monte Carlo methods
Integration
Boundary value problems for PDE's
Numerics of stochastic differential equations
Simulation of random variables, stochastic processes and fields

Article formats
Research articles

> Information on submission process

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Your benefits:

In-depth discussions crossing the boundaries of many disciplines
State-of-the-art research on theory and applications of Monte Carlo Methods
Rigorous peer-review
International and renowned editorial board

Open Access
Moving permuted congruential generators beyond linear congruential generators

1. Oktober 2025

Christopher Draper, Michael Mascagni

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The permuted congruential generators is a set of pseudorandom number generators released by Melissa E. O’Neill in 2014. The original technical report outlined several lightweight scrambling techniques designed for the linear congruential generator. Each scrambling technique offered some improvement to the quality of the linear congruential generator. However, the real strength of the scrambling techniques was that they could be combined into multiple overall stronger scramblers. The technical report concludes with the creation of the PCG library, a popular pseudorandom number generation library that implements several generators described in the technical report. Starting from the observation that the paper’s work was narrowly focused on implementing their scrambling techniques for specific linear congruential generators, we explore the permuted congruential generator scrambling techniques and their potential for being applied to other pseudorandom number generators by generalizing the scrambling techniques to work across different pseudorandom number generators.
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GMM estimation and asymptotic properties in periodic GARCH(1, 1) models

1. Oktober 2025

Ines Lescheb

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In this paper, we study the class of first order Periodic Generalized Autoregressive Conditional heteroscedasticity processes ( PGARCH ⁢ ( 1 , 1 ) {\mathrm{PGARCH}(1,1)} for short) in which the parameters in the volatility process are allowed to switch between different regimes. First, we establish necessary and sufficient conditions for a PGARCH ⁢ ( 1 , 1 ) {\mathrm{PGARCH}(1,1)} process to have a unique stationary solution (in periodic sense) and for the existence of moments of any order. Next, we are able to estimate the unknown parameters involved in model via the so-called generalized method of moments (GMM). We construct an estimator and establish its asymptotic properties. Specifically, we demonstrate its consistency and asymptotic normality. The GMM estimator in some cases can be more efficient than the least squares estimator (LSE) and the quasi maximum likelihood estimator (QMLE). Some simulation studies are also performed to highlight the impact of our theoretical results.
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Applying non-informative G-prior for logistic regression models with different patterns of data points

1. Juli 2025

Huong T. T. Pham, Hoa Pham, Kai Siong Yow

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In logistic regression models, different patterns of data points in observed data can cause large bias in parameter estimates, especially when separation is present in the observed data. In the frequentist approach, maximum likelihood estimates fail to exist when separation occurs in the observed data. In the Bayesian approach, the existence of posterior means is also affected by the presence of separation depending on the form of prior distributions. In this paper, a non-informative G-prior for Bayesian method is proposed to reduce the bias of the parameter estimation when prior distributions of parameters do not have information and separation is present in the data. In this proposed method, the information from observed data and ideas of a normal regression model are implemented to form the mean and standard deviation of the normal prior distributions. The Markov chain Monte Carlo algorithm is then employed by using Metropolis Hasting algorithm to sample for the target posterior distribution. Results show that estimates from the proposed Bayesian method are more accurate and reliable than from the classical approach when separation is present or is not present in the observed data. Moreover, the proposed Bayesian method can provide better estimated results compared to the default Cauchy prior Bayesian approach when the prior distribution does not have information. The proposed method is also validated by applying it to a case study of MROZ data.
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Antithetic variates revisited again

1. Januar 2000

Reiichiro Kawai

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We revisit the method of antithetic variates, perhaps the simplest yet profound variance reduction technique among many others, with the aim of comprehensively improving the method in its general formulation in the seminal works A new Monte Carlo technique: Antithetic variates [Hammersley and Morton, Math. Proc. Cambridge Philos. Soc. 52 (1956), 449–475] and Antithetic variates revisited [Fishman and Huang, Commun. ACM 26 (1983), 964–971]. The achieved advancement under this general formulation contrasts with the conventional approach based on equally weighted two variates with negative correlation, commonly referred to as the method of antithetic variates in various contexts. In pursuit of the aim, we investigate its second-order structure in depth and introduce an adaptive algorithm designed to optimize the weights among multiple variates throughout the primary Monte Carlo estimation process. In order to effectively demonstrate the theoretical advancements, we present numerical results throughout the presentation, vividly showcasing the potential effectiveness of the proposed approach and adaptive algorithm in the face of varying weights.
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Stochastic iterative refinement with preconditioning for solving Helmholtz equation via boundary integral equation

1. Januar 2000

Karl K. Sabelfeld, Alexander Prokopiev

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This work suggests different Monte Carlo algorithms for solving large systems of linear algebraic equations arising from the numerical solution of the Dirichlet problem for the Helmholtz equation. Approach based on boundary integral representations, vector randomization algorithm, method of fundamental solutions, stochastic projection algorithm, and randomized singular value decomposition are applied. It is shown that the use of stochastic iterative refinement and preconditioning can significantly improve the accuracy and stability of the computations. Simulation results are presented, demonstrating the effectiveness of the proposed methods.
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Linear estimation and prediction for the generalized Bilal distribution with application to thermal conductivity data

1. Januar 2000

Zuber Akhter, Ehsan Ormoz, S. M. T. K. MirMostafaee

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This study develops explicit algebraic expressions for the single and product moments of order statistics derived from the generalized Bilal (GB) distribution. These expressions facilitate the computation of means, variances and covariances of order statistics for sample sizes up to n = 10 {n=10} with specified parameter values. The derived moments serve as the foundation for constructing the best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) for the location and scale parameters applicable to both complete and type-II right censored samples. Additionally, the study explores the prediction of unobserved order statistics in type-II right censored samples. The theoretical results are validated through a simulation study, while a real data example highlights their practical utility. These findings establish a robust framework for statistical inference based on order statistics from the GB distribution.
Open Access
An overview of financial mathematics with Python codes

1. Januar 2000

Nikolaos Halidias

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In this note we will discuss and review some recent results concerning well-known financial mathematical problems such as portfolio construction, dynamic trading, option pricing, etc. We will use some Python codes concerning the above and we will compare the results with the existing methods and techniques. We propose also a new type of multi-asset options; the options on correlation. Using this kind of options one can refine more effectively the profit function of his/her portfolio when this contain two or more assets. It is mathematically certain that, in practice, someone will eventually apply the techniques described in this paper. This is because, regarding the portfolio construction problem, we allow the investor to employ any forecasting technique – e.g., statistical methods, machine learning, behavioral finance, intuition, etc. Subsequently, the investor can enhance both the return and safety of their portfolio by incorporating call and put options. In contrast, for the derivative pricing problem, it is evident that there is no room for forecasts (see volatility for example), as pricing involves two counterparties – the seller and the buyer – making it, metaphorically, a dance for two. For this reason, the pricing methodology proposed in this paper is model-free, ensuring that the resulting prices are fully consistent with the market values of available contracts. Moreover, the investor decides at which price to buy or sell a contract based on practical, statically implementable hedging strategies that we propose in this work. That is, any pricing method should justify why an investor ought to buy or sell a derivative at the proposed price. In other words, the method must provide a clear, economically sound rationale-typically grounded in no-arbitrage principles, replication arguments, or explicit hedging strategies – that links the quoted price to actionable, implementable decisions for market participants. What remains to be explored are advanced forecasting techniques that account for events affecting the stocks of interest to the investor, as well as the documentation of hedging strategies for path-dependent options.

Journal Impact Factor	0.6	2024, Journal Citation Reports (Clarivate, 2025)
5-year Journal Impact Factor	0.8	2024, Journal Citation Reports (Clarivate, 2025)
Journal Citation Indicator	0.31	2024, Journal Citation Reports (Clarivate, 2025)
CiteScore	1.4	2024, Scopus (Elsevier B.V., 2025)
SCImago Journal Rank	0.379	2024, SJR (Scimago Lab, 2025; Data Source: Scopus)
Source Normalized Impact per Paper	0.767	2024, CWTS Journal Indicators (CWTS B.V., 2025; Data Source: Scopus)
Mathematical Citation Quotient	0.10

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Managing Editor
Karl K. Sabelfeld 
Institute of Computational Mathematics and Mathematical Geophysics
Academy of Sciences
Siberian Branch
Lavrentjeva 6
630090 Novosibirsk, Russia
E-mail: karl@osmf.sscc.ru, sabelfeld.karl@yahoo.de
 
Editorial Board
Kurt Binder 
Institut für Physik
Johannes Gutenberg Universität Mainz
Staudinger Weg 7
55099 Mainz, Germany
E-mail: binder@chaplin.physik.uni-mainz.de

Nicolas Bouleau 
Ecoles des Ponts
28 rue des Saints Peres
75007 Paris, France
E-mail: nb@enpc.fr

Alexandre J. Chorin 
Department of Mathematics
University of California
Berkeley, CA 94720-3840, USA
E-mail: chorin@math.berkeley.edu

Ivan Dimov 
Bulgarian Academy of Sciences
Acad. G. Bonchev St. 25A
1113 Sofia, Bulgaria
E-mail: ivdimov@bas.org

Alain Dubus 
Service de Metrologie Nucleaire CP165/84
Université Libre de Bruxelles
Av. F.D. Roosevelt 50
1050 Brussels, Belgium
E-mail: adubus@ulb.ac.be

Alexander D. Egorov 
Belarus Academy of Sciences
Surganova St. 11
Minsk 220072, Belarus
E-mail: egorov@im.bas-net.by

Sergei M. Ermakov 
Department of Mathematics and Mechanics
St. Petersburg State University
Bibliotechnaya Sq. 2
Petrodvorets
198904 St. Petersburg, Russia
E-mail: sergej.ermakov@pobox.spbu.ru

John H. Halton 
University of North Carolina
305 Sitterson Hall
C.B. 3175 Chapel Hill
NC 27599-3175, USA
E-mail: halton@cs.unc.edu

Stefan Heinrich 
Universität Kaiserslautern
Postfach 3049
67653 Kaiserslautern, Germany
E-mail: heinrich@informatik.uni-kl.de

Chi-Ok Hwang
School of Liberal Arts and Sciences
Gwangju Institute of Science and Technology
Gwangju, 61005 Republic of Korea
E-mail: chwang@gist.ac.kr

Malvin H. Kalos 
Lawrence Livermore National Laboratory
Livermore, CA 94551, USA

Dmitry R., Kolyukhin
Trofimuk Institute of Petroleum Geology and Geophysics SB RAS,
3 Koptug ave.
630090 Novosibirsk, Russia
E-mail: KolyukhinDR@ipgg.sbras.ru

Dominique Lepingle 
Department of Mathematics
University of Orléans
B.P. 6759
45067 Orléans cedex 2, France
E-mail: lepingle@labomath.univ-orleans.fr

Yaohang Li
Department of Computer Science
Old Dominion University
4700 Elkhorn Ave, Suite 3300
Norfolk, VA 23529-0162
USA
yaohang@cs.odu.edu

Roman Makarov 
Department of Mathematics
Wilfrid Laurier University
75 University Avenue West
Waterloo, Ontario N2L 3C5, Canada
E-mail: rmakarov@wlu.ca

Michael Mascagni 
Department of Computer Science
Florida State University
203 Love Building
Tallahassee, FL 32306-4530, USA
E-mail: mascagni@cs.fsu.edu

Peter Mathé 
Weierstraß-Institut für Angewandte Analysis und Stochastik
Mohrenstr. 39
10117 Berlin, Germany
E-mail: mathe@wias-berlin.de

Harald Niederreiter 
Austrian Academy of Sciences
Dr. Ignaz Seipel-Platz 2
1010 Wien
E-mail: Harald.Niederreiter@oeaw.ac.at

Shigeyoshi Ogawa 
Department of Mathematics
Ritsumeikan University
Kyoto, Japan
E-mail: ogawa-s@se.ritsumei.ac.jp

Giray Ökten 
Department of Mathematics
Florida State University
Tallahassee, FL 32306-4510, USA
E-mail: okten@math.fsu.edu

Eckhard Platen 
School of Finance and Economics
University of Technology, Sydney
PO Box 123
Broadway NSW 2007, Australia
E-mail: eckhard.platen@uts.edu.au

Brian R. Sawford 
Department of Mechanical Engineering
Monash University
Building 33
Clayton Campus
Wellington Road
Clayton, VIC 3800, Australia
E-mail: brian.sawford@.eng.monash.au

Wolfgang C. Schmid 
Department of Mathematics
University of Salzburg
Hellbrunnerstr. 34
5020 Salzburg, Austria
E-mail: wolfgang.schmid@sbg.ac.at

John Schoenmakers 
Weierstraß-Institut für Angewandte Analysis und Stochastik
Mohrenstr. 39
10117 Berlin, Germany.
E-mail: schoenma@wias-berlin.de

Irina A. Shalimova
Institute of Computational Mathematics and Mathematical Geophysics,
Russian Acad.Sci,
6 Lavrentiev str.,
630090, Novosibirsk, Russia
E-mail: ias@osmf.sscc.ru

Ilya M. Sobol 
Institute for Mathematical Modelling
Russian Academy of Sciences
Miusskaya Square 4
125047 Moscow, Russia
E-mail: sobol@ciam.ru

Jerry Spanier 
Beckman Laser Institute & Medical Cliic
1002 Health Sciences Road East
Irvine, CA 92612, USA
E-mail: jerome.spanier@cgu.edu

Denis Talay 
INRIA
2004 Route des Lucioles
B.P. 109
06561 Valbonne cedex, France
E-mail: talay@sophia.inria.fr

Wolfgang Wagner 
Weierstraß-Institut für Angewandte Analysis und Stochastik
Mohrenstr. 39
10117 Berlin, Germany
E-mail: wagner@wias-berlin.de

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eISSN:

1569-3961

ISSN:

0929-9629

Sprache:

Englisch

Verlag:

De Gruyter

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Erstveröffentlichung:

1. Januar 1995

Erscheinungsweise:

4 Hefte pro Jahr

eISSN: 1569-3961

ISSN: 0929-9629

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