ORCID Profile
0000-0002-3845-015X
Current Organisation
University of Tokyo
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Publisher: Bernoulli Society for Mathematical Statistics and Probability
Date: 02-2007
DOI: 10.3150/07-BEJ5034
Publisher: Elsevier BV
Date: 04-2011
Publisher: Springer Science and Business Media LLC
Date: 24-06-2023
Publisher: Informa UK Limited
Date: 25-09-2023
Publisher: Infopro Digital Services Limited
Date: 2018
Publisher: Elsevier BV
Date: 02-2022
Publisher: Elsevier BV
Date: 11-2022
Publisher: IEEE
Date: 12-2009
Publisher: Informa UK Limited
Date: 20-05-2015
Publisher: Elsevier BV
Date: 03-2022
Publisher: Informa UK Limited
Date: 27-07-2010
Publisher: Elsevier BV
Date: 12-2012
Publisher: Informa UK Limited
Date: 05-2013
Publisher: Association for Computing Machinery (ACM)
Date: 04-2010
Abstract: To enhance efficiency in Monte Carlo simulations, we develop an adaptive stratified s ling algorithm for allocation of s ling effort within each stratum, in which an adaptive variance reduction technique is applied. Given the number of replications in each batch, our algorithm updates allocation fractions to minimize the work-normalized variance of the stratified estimator of the mean. We establish the asymptotic normality of the stratified estimator of the mean as the number of batches tends to infinity. Although implementation of the proposed algorithm requires a small amount of initial work, the algorithm has the potential to yield substantial improvements in estimator efficiency. Equally important is that the adaptive framework avoids the need for frequent recalibration of the parameters of the variance reduction methods applied within each stratum when changes occur in the experimental conditions governing system performance. To illustrate the applicability and effectiveness of our algorithm, we provide numerical results for a Black--Scholes option pricing, where we stratify the underlying Brownian motion with respect to its terminal value and apply an importance s ling method to normal random variables filling in the Brownian path. Relative to the estimator variance with proportional allocation, the proposed algorithm achieved a fourfold reduction in estimator variance with a negligible increase in computing time.
Publisher: No publisher found
Date: 2016
Publisher: IOP Publishing
Date: 04-02-2020
Publisher: Elsevier BV
Date: 08-2017
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2020
DOI: 10.1137/18M1232231
Publisher: Springer Science and Business Media LLC
Date: 25-10-2013
Publisher: Springer Science and Business Media LLC
Date: 05-11-2012
Publisher: AIP Publishing
Date: 09-2021
DOI: 10.1063/5.0054330
Abstract: A variety of real life phenomena exhibit complex time-inhomogeneous nonlinear diffusive motion in the presence of an external harmonic force. In capturing the characteristics of such dynamics, the class of Ornstein–Uhlenbeck processes, with its physical time appropriately modulated, has long been regarded as the most relevant model on the basis of its mean reversion property. In this paper, we contrast two similar, yet definitely different, time-changing mechanisms in harmonic force fields by systematically deriving and presenting a variety of key properties all at once, that is, whether or not and how those time-changing mechanisms affect the characteristics of mean-reverting diffusion through s le path properties, the marginal probability density function, the asymptotic degeneracy of increments, the stationary law, the second-order structure, and the ensemble- and time-averaged mean square displacements. Some of those properties turn out rather counter-intuitive due to, or irrespective of, possible degeneracy of time-changing mechanisms in the long run. In light of those illustrative comparisons, we examine whether such time-changing operations are worth the additional operational cost, relative to physically relevant characteristics induced, and deduce practical implications and precautions from modeling and inference perspectives, for instance, on the experimental setup involving those anomalous diffusion processes, such as the observation start time and stepsize when measuring mean square displacements, so as to preclude potentially misleading results and paradoxical interpretations.
Publisher: Walter de Gruyter GmbH
Date: 21-01-2007
Publisher: American Physical Society (APS)
Date: 13-02-2012
Publisher: Elsevier BV
Date: 07-2021
Publisher: Informa UK Limited
Date: 2012
Publisher: Wiley
Date: 10-2011
Publisher: Informa UK Limited
Date: 08-2009
Publisher: World Scientific Pub Co Pte Lt
Date: 05-2009
DOI: 10.1142/S0219024909005294
Abstract: Monte Carlo estimators of sensitivity indices and the marginal density of the price dynamics are derived for the Hobson-Rogers stochastic volatility model. Our approach is based mainly upon the Kolmogorov backward equation by making full use of the Markovian property of the dynamics given the past information. Some numerical ex les are presented with a GARCH-like volatility function and its extension to illustrate the effectiveness of our formulae together with a clear exhibition of the skewness and the heavy tails of the price dynamics.
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2017
DOI: 10.1137/15M1047192
Publisher: American Physical Society (APS)
Date: 20-06-2019
Publisher: Association for Computing Machinery (ACM)
Date: 28-02-2023
DOI: 10.1145/3573386
Abstract: Adaptive Monte Carlo variance reduction is an effective framework for running a Monte Carlo simulation along with a parameter search algorithm for variance reduction, whereas an initialization step is required for preparing problem parameters in some instances. In spite of the effectiveness of adaptive variance reduction in various fields of application, the length of the preliminary phase has often been left unspecified for the user to determine on a case-by-case basis, much like in typical sequential frameworks. This uncertain element may possibly be even fatal in realistic finite-budget situations, since the pilot run may take most of the budget, or possibly use up all of it. To unnecessitate such an ad hoc initialization step, we develop a batching procedure in adaptive variance reduction, and provide an implementable formula of the learning rate in the parameter search which minimizes an upper bound of the theoretical variance of the empirical batch mean. We analyze decay rates of the minimized upper bound towards the minimal estimator variance with respect to the predetermined computing budget, and provide convergence results as the computing budget increases progressively when the batch size is fixed. Numerical ex les are provided to support theoretical findings and illustrate the effectiveness of the proposed batching procedure.
Publisher: Elsevier BV
Date: 08-2006
Publisher: Elsevier BV
Date: 03-2023
Publisher: Elsevier BV
Date: 2010
Publisher: The Royal Society
Date: 08-02-2012
Abstract: The random search problem has long attracted continuous interest owing to its broad interdisciplinary range of applications, including animal foraging, facilitated target location in biological systems and human motion. In this paper, we address the issue of statistical inference for ordinary Gaussian, Pareto, tempered Pareto and fractional Gaussian random walk models, which are among the most studied random walk models proposed as the best strategy in the random search problem. Based on rigorous analysis of the local asymptotic normality property and the Fisher information, we discuss some issues in unbiased joint estimation of the model parameters, in particular, the maximum-likelihood estimation. We present that there exist both theoretical and practical difficulties in more realistic tempered Pareto and fractional Gaussian random walk models from a statistical standpoint. We discuss our findings in the context of in idual animal movement and show how our results may be used to facilitate the analysis of movement data and to improve the understanding of the underlying stochastic process.
Publisher: Walter de Gruyter GmbH
Date: 2011
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2015
DOI: 10.1137/151004070
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2013
DOI: 10.1137/110841497
Publisher: Informa UK Limited
Date: 05-08-2015
Publisher: Informa UK Limited
Date: 08-2013
Publisher: Springer Berlin Heidelberg
Date: 2010
Publisher: Elsevier BV
Date: 03-2020
Publisher: Elsevier BV
Date: 05-2011
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 28-04-2023
DOI: 10.1137/21M1430996
Publisher: IOP Publishing
Date: 02-12-2023
Abstract: We investigate the fractional Fokker-Planck equation subject to a d ing force with an emphasis on its dimension dependent properties. We reveal a variety of surprising properties of its solution through the lens of the probability density function of the corresponding stochastic process with nonlinear mean square displacements, such as existence, singularity, regularity, modality, stationarity and second-order structure, which are largely dependent on the dimension and the random clock. Taking into account that the trajectory information is most often collected from multidimensional systems, the discovered facts have the potential to play important roles as key foundations and alerts for inference, model identification and prediction, when departing from the well-understood univariate framework.
Publisher: Elsevier BV
Date: 04-2023
Publisher: Springer Science and Business Media LLC
Date: 11-11-2015
Publisher: World Scientific Pub Co Pte Lt
Date: 02-2018
DOI: 10.1142/S0219024918500097
Abstract: We introduce a new approach for systematically obtaining smooth deterministic upper bounds for the price function of American style options. These bounding functions are characterized by sufficient conditions, under which the bounds may be infimized. In a single implementation, the proposed approach obtains explicit bounds in the form of piecewise polynomial functions, which bound the price function from above over the whole problem domain both in time and state. As a consequence, these global bounds store a continuum of information in the form of a finite number of polynomial coefficients. The proposed approach achieves these bounds, free from statistical error, without recourse to s le path simulation, without truncating the naturally unbounded domain that arises in this problem, and without discretizing the time and state variables. Throughout the paper, we demonstrate the effectiveness of the proposed method in obtaining tight upper bounds for American style option prices in a variety of market models and with various payoff structures, such as the multivariate Black Scholes and Heston stochastic volatility models and the American put and butterfly payoff structures. We also discuss extensions of the proposed methodology to perpetual American style options and frameworks in which the underlying asset contains jumps.
Publisher: Springer Berlin Heidelberg
Date: 2012
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2018
DOI: 10.1137/18M1173472
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2010
DOI: 10.1137/090752365
Publisher: Elsevier BV
Date: 02-2011
Publisher: EDP Sciences
Date: 06-12-2013
DOI: 10.1051/PS/2011101
Publisher: Elsevier BV
Date: 03-2023
Publisher: Informa UK Limited
Date: 31-01-2011
Publisher: Elsevier BV
Date: 07-2023
Publisher: IOP Publishing
Date: 23-05-2012
Publisher: IOP Publishing
Date: 03-2019
Publisher: Institute of Mathematical Statistics
Date: 2023
DOI: 10.1214/23-PS18
Publisher: Elsevier BV
Date: 12-2015
Publisher: Springer Science and Business Media LLC
Date: 17-08-2008
Publisher: Institute of Mathematical Statistics
Date: 2021
DOI: 10.1214/20-PS359
Publisher: IOP Publishing
Date: 16-05-2017
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2008
DOI: 10.1137/070680564
Publisher: Elsevier BV
Date: 12-2013
Publisher: Springer Science and Business Media LLC
Date: 20-08-2016
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2017
DOI: 10.1137/17M111482X
Publisher: Elsevier BV
Date: 11-2011
Publisher: Universiti Malaysia Pahang Publishing
Date: 30-12-2014
Location: United Kingdom of Great Britain and Northern Ireland
Start Date: 2021
End Date: 2026
Funder: Japan Society for the Promotion of Science
View Funded ActivityStart Date: 2008
End Date: 2009
Funder: Japan Society for the Promotion of Science
View Funded ActivityStart Date: 2020
End Date: 2022
Funder: Japan Society for the Promotion of Science
View Funded ActivityStart Date: 2009
End Date: 2011
Funder: Japan Society for the Promotion of Science
View Funded Activity