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Dissertations / Theses on the topic 'Monte Carlo method'

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Published: 4 June 2021

Last updated: 12 October 2024

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1

Janzon, Krister. "Monte Carlo Path Simulation and the Multilevel Monte Carlo Method." Thesis, Umeå universitet, Institutionen för fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-151975.

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A standard problem in the field of computational finance is that of pricing derivative securities. This is often accomplished by estimating an expected value of a functional of a stochastic process, defined by a stochastic differential equation (SDE). In such a setting the random sampling algorithm Monte Carlo (MC) is useful, where paths of the process are sampled. However, MC in its standard form (SMC) is inherently slow. Additionally, if the analytical solution to the underlying SDE is not available, a numerical approximation of the process is necessary, adding another layer of computational complexity to the SMC algorithm. Thus, the computational cost of achieving a certain level of accuracy of the estimation using SMC may be relatively high. In this thesis we introduce and review the theory of the SMC method, with and without the need of numerical approximation for path simulation. Two numerical methods for path approximation are introduced: the Euler–Maruyama method and Milstein's method. Moreover, we also introduce and review the theory of a relatively new (2008) MC method – the multilevel Monte Carlo (MLMC) method – which is only applicable when paths are approximated. This method boldly claims that it can – under certain conditions – eradicate the additional complexity stemming from the approximation of paths. With this in mind, we wish to see whether this claim holds when pricing a European call option, where the underlying stock process is modelled by geometric Brownian motion. We also want to compare the performance of MLMC in this scenario to that of SMC, with and without path approximation. Two numerical experiments are performed. The first to determine the optimal implementation of MLMC, a static or adaptive approach. The second to illustrate the difference in performance of adaptive MLMC and SMC – depending on the used numerical method and whether the analytical solution is available. The results show that SMC is inferior to adaptive MLMC if numerical approximation of paths is needed, and that adaptive MLMC seems to meet the complexity of SMC with an analytical solution. However, while the complexity of adaptive MLMC is impressive, it cannot quite compensate for the additional cost of approximating paths, ending up roughly ten times slower than SMC with an analytical solution.

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2

Lacasse, Martin Daniel. "New dynamical Monte Carlo renormalization group method." Thesis, McGill University, 1990. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=60062.

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The kinetics of a phase transition has been studied by using a new dynamical Monte Carlo renormalization group method. Using a majority rule block-spin transformation in both space and contiguous times, we numerically renormalized the evolving configurations during the phase separation of a kinetic Ising model with spin-flip dynamics. We find that, in the scaling regime, the average domain size R(t) grows in time consistently with the $R sim t sp{1/2}$ Allen-Cahn antiphase boundary motion theory, although some correcting factors may exist. The same procedure has also been applied to the corresponding equilibrium critical system in order to find the critical exponent z. Our method yields values that are consistent with the ones obtained from a finite-size scaling analysis applied on the same data, thus showing that, in principle, this method can be successfully used to determine z in a more precise and consistent way.

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3

Zhang, Yichuan. "Scalable geometric Markov chain Monte Carlo." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20978.

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Markov chain Monte Carlo (MCMC) is one of the most popular statistical inference methods in machine learning. Recent work shows that a significant improvement of the statistical efficiency of MCMC on complex distributions can be achieved by exploiting geometric properties of the target distribution. This is known as geometric MCMC. However, many such methods, like Riemannian manifold Hamiltonian Monte Carlo (RMHMC), are computationally challenging to scale up to high dimensional distributions. The primary goal of this thesis is to develop novel geometric MCMC methods applicable to large-scale problems. To overcome the computational bottleneck of computing second order derivatives in geometric MCMC, I propose an adaptive MCMC algorithm using an efficient approximation based on Limited memory BFGS. I also propose a simplified variant of RMHMC that is able to work effectively on larger scale than the previous methods. Finally, I address an important limitation of geometric MCMC, namely that is only available for continuous distributions. I investigate a relaxation of discrete variables to continuous variables that allows us to apply the geometric methods. This is a new direction of MCMC research which is of potential interest to many applications. The effectiveness of the proposed methods is demonstrated on a wide range of popular models, including generalised linear models, conditional random fields (CRFs), hierarchical models and Boltzmann machines.

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4

Veld, Pieter Jacob in 't. "Monte Carlo studies of liquid structure /." Digital version:, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p9992826.

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5

Hazelton, Martin Luke. "Method of density estimation with application to Monte Carlo methods." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334850.

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6

Lefebvre, Geneviève 1978. "Practical issues in modern Monte Carlo integration." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103209.

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Computing marginal likelihoods to perform Bayesian model selection is a challenging task, particularly when the models considered involve a large number of parameters. In this thesis, we propose the use of an adaptive quadrature algorithm to automate the selection of the grid in path sampling, an integration technique recognized as one of the most powerful Monte Carlo integration statistical methods for marginal likelihood estimation. We begin by examining the impact of two tuning parameters of path sampling, the choice of the importance density and the specification of the grid, which are both shown to be potentially very influential. We then present, in detail, the Grid Selection by Adaptive Quadrature (GSAQ) algorithm for selecting the grid. We perform a comparison between the GSAQ and standard grid implementation of path sampling using two well-studied data sets; the GSAQ approach is found to yield superior results. GSAQ is then successfully applied to a longitudinal hierarchical regression model selection problem in Multiple Sclerosis research.
Using an identity arising in path sampling, we then derive general expressions for the Kullback-Leibler (KL) and Jeffrey (J) divergences between two distributions with common support but from possibly different parametric families. These expressions naturally stem from path sampling when the popular geometric path is used to link the extreme densities. Expressions for the KL and J-divergences are also given for any two intermediate densities lying on the path. Estimates for the KL divergence (up to a constant) and for the J-divergence, between a posterior distribution and a selected importance density, can be obtained directly, prior to path sampling implementation. The J-divergence is shown to be helpful for choosing importance densities that minimize the error of the path sampling estimates.
Finally we present the results of a simulation study devised to investigate whether improvement in performance can be achieved by using the KL and J-divergences to select sequences of distributions in parallel (population-based) simulations, such as in the Sequential Monte Carlo Sampling and the Annealed Importance Sampling algorithms. We compare these choices of sequences to more conventional choices in the context of a mixture example. Unexpected results are obtained, and those for the KL and J-divergences are mixed. More fundamentally, we uncover the need to select the sequence of tempered distributions in accordance with the resampling scheme.

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7

Lee, Ming Ripman, and 李明. "Monte Carlo simulation for confined electrolytes." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31240513.

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8

Lee, Ming Ripman. "Monte Carlo simulation for confined electrolytes /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22055009.

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9

Yam, Chiu Yu. "Quasi-Monte Carlo methods for bootstrap." HKBU Institutional Repository, 2000. http://repository.hkbu.edu.hk/etd_ra/272.

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10

Wong, Ping-yung. "Molecular clusters on surfaces : a Monte Carlo study /." Hong Kong : University of Hong Kong, 1999. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20566694.

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11

Obradovic, Borna Josip. "Multi-dimensional Monte Carlo simulation of ion implantation into complex structures /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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12

Booth, G. H. "A novel quantum Monte Carlo method for molecular systems." Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596772.

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This thesis is concerned with the development of a new ab initio Monte Carlo method for the evaluation of exact, basis set correlation energies. A simple set of rules acting on signed walkers allow for the simulation of the underlying imaginary-time Schrödinger equation in a finite space of Slater determinants. These rules return probabilistic events which are stochastically realised in each step of the algorithm. The antisymmetric space in which the dynamic operates precludes the emergence of Bosonic solutions, and the Fermion sign problem is countered without approximation by inclusion of annihilation events between walkers of different sign. The method is applied to many molecular systems described by common Gaussian basis sets. Single point calculations, binding curves, basis set expansions and detailed studies of ionisation potentials are included. In these investigations, the method is compared to several alternative quantum chemical methods as well as exact full configuration interaction results to asses its qualities. The method is found to significantly reduce the memory and CPU requirements compared to exact diagonalisation methods, and includes an effective parallelisation scheme which scales almost linearly up to thousands of processors. This extends the scope of exact multireference calculations and allows for larger systems than previously possible to be treated.

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13

Vaičiulytė, Ingrida. "Study and application of Markov chain Monte Carlo method." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20141209_112440-55390.

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Markov chain Monte Carlo adaptive methods by creating computationally effective algorithms for decision-making of data analysis with the given accuracy are analyzed in this dissertation. The tasks for estimation of parameters of the multivariate distributions which are constructed in hierarchical way (skew t distribution, Poisson-Gaussian model, stable symmetric vector law) are described and solved in this research. To create the adaptive MCMC procedure, the sequential generating method is applied for Monte Carlo samples, introducing rules for statistical termination and for sample size regulation of Markov chains. Statistical tasks, solved by this method, reveal characteristics of relevant computational problems including MCMC method. Effectiveness of the MCMC algorithms is analyzed by statistical modeling method, constructed in the dissertation. Tests made with sportsmen data and financial data of enterprises, belonging to health-care industry, confirmed that numerical properties of the method correspond to the theoretical model. The methods and algorithms created also are applied to construct the model for sociological data analysis. Tests of algorithms have shown that adaptive MCMC algorithm allows to obtain estimators of examined distribution parameters in lower number of chains, and reducing the volume of calculations approximately two times. The algorithms created in this dissertation can be used to test the systems of stochastic type and to solve other statistical... [to full text]
Disertacijoje nagrinėjami Markovo grandinės Monte-Karlo (MCMC) adaptavimo metodai, skirti efektyviems skaitiniams duomenų analizės sprendimų priėmimo su iš anksto nustatytu patikimumu algoritmams sudaryti. Suformuluoti ir išspręsti hierarchiniu būdu sudarytų daugiamačių skirstinių (asimetrinio t skirstinio, Puasono-Gauso modelio, stabiliojo simetrinio vektoriaus dėsnio) parametrų vertinimo uždaviniai. Adaptuotai MCMC procedūrai sukurti yra pritaikytas nuoseklaus Monte-Karlo imčių generavimo metodas, įvedant statistinį stabdymo kriterijų ir imties tūrio reguliavimą. Statistiniai uždaviniai išspręsti šiuo metodu leidžia atskleisti aktualias MCMC metodų skaitmeninimo problemų ypatybes. MCMC algoritmų efektyvumas tiriamas pasinaudojant disertacijoje sudarytu statistinio modeliavimo metodu. Atlikti eksperimentai su sportininkų duomenimis ir sveikatos industrijai priklausančių įmonių finansiniais duomenimis patvirtino, kad metodo skaitinės savybės atitinka teorinį modelį. Taip pat sukurti metodai ir algoritmai pritaikyti sociologinių duomenų analizės modeliui sudaryti. Atlikti tyrimai parodė, kad adaptuotas MCMC algoritmas leidžia gauti nagrinėjamų skirstinių parametrų įvertinius per mažesnį grandžių skaičių ir maždaug du kartus sumažinti skaičiavimų apimtį. Disertacijoje sukonstruoti algoritmai gali būti pritaikyti stochastinio pobūdžio sistemų tyrimui ir kitiems statistikos uždaviniams spręsti MCMC metodu.

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14

Armour, Jessica D. "On the Gap-Tooth direct simulation Monte Carlo method." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/72863.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, February 2012.
"February 2012." Cataloged from PDF version of thesis.
Includes bibliographical references (p. [73]-74).
This thesis develops and evaluates Gap-tooth DSMC (GT-DSMC), a direct Monte Carlo simulation procedure for dilute gases combined with the Gap-tooth method of Gear, Li, and Kevrekidis. The latter was proposed as a means of reducing the computational cost of microscopic (e.g. molecular) simulation methods using simulation particles only in small regions of space (teeth) surrounded by (ideally) large gaps. This scheme requires an algorithm for transporting particles between teeth. Such an algorithm can be readily developed and implemented within direct Monte Carlo simulations of dilute gases due to the non-interacting nature of the particle-simulators. The present work develops and evaluates particle treatment at the boundaries associated with diffuse-wall boundary conditions and investigates the drawbacks associated with GT-DSMC implementations which detract from the theoretically large computational benefit associated with this algorithm (the cost reduction is linear in the gap-to-tooth ratio). Particular attention is paid to the additional numerical error introduced by the gap-tooth algorithm as well as the additional statistical uncertainty introduced by the smaller number of particles. We find the numerical error introduced by transporting particles to adjacent teeth to be considerable. Moreover, we find that due to the reduced number of particles in the simulation domain, correlations persist longer, and thus statistical uncertainties are larger than DSMC for the same number of particles per cell. This considerably reduces the computational benefit associated with the GT-DSMC algorithm. We conclude that the GT-DSMC method requires more development, particularly in the area of error and uncertainty reduction, before it can be used as an effective simulation method.
by Jessica D. Armour.
S.M.

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15

Fernandez-Carmona, Juan. "Modelling protein backbone loops using the Monte Carlo method." Thesis, University of Southampton, 2009. https://eprints.soton.ac.uk/173851/.

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Novel methods that perform local moves such as the gaussian bias or Con- certed Rotation with Angles, increase the exploration of the conformational phase space. These methods have been applied successfully to small systems, and have proved to be more efficient than the classical Monte Carlo method. The main aim of my work was to study and include backbone moves for proteins, such as the Concerted Rotation with Angle (CRA) and the gaussian bias in the ProtoMS package. The CRA was then applied to several systems of biological interest to compute relative binding free energies and conformational changes to obtain insights into the binding mode and system flexibility. The CRA algorithm has been used to sample biological systems such as lysozyme L99A mutant, Bcr-Abl kinases and PDE5 phosphodiesterase and led to increased sampling of the backbone and more precise free energy results.

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16

Zheng, Zhongrong. "Analysis of swapping and tempering Monte Carlo algorithms." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0006/NQ43460.pdf.

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17

Stephen, Alexander. "Enhancement of thermionic cooling using Monte Carlo simulation." Thesis, University of Aberdeen, 2014. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=210113.

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Advances in the field of semiconductor physics have allowed for rapid development of new, more powerful devices. The new fabrication techniques allow for reductions in device geometry, increasing the possible wafer packing density. The increased output power comes with the price of excessive heat generation, the removal of which proves problematic at such scales for conventional cooling systems. Consequently, there is a rising demand for new cooling systems, preferably those that do not add large amount of additional bulk to the system. One promising system is the thermoelectric (TE) cooler which is small enough to be integrated onto the device wafer. Unlike more traditional gas and liquid coolers, TE coolers do not require moving parts or external liquid reservoirs, relying only on the flow of electrons to transport heat energy away from the device. Although TE cooling provides a neat solution for the extraction of heat from micron scale devices, it can normally only produce small amounts of cooling of 1-2 Kelvin, limiting its application to low power devices. This research aimed to find ways to enhance the performance of the TE cooler using detailed simulation analysis. For this, a self consistent, semi-classical, ensemble Monte Carlo model was designed to investigate the operation of the TE cooler at a higher level than would be possible with experimental measurements alone. As part of its development, the model was validated on a variety of devices including a Gunn diode and two micro-cooler designs from the literature, one which had been previously simulated and another which had been experimentally analysed. When applied to the TE cooler of focus, novel operational data was obtained and signification improvements in cooling power were found with only minor alterations to the device structure and without need for an increase in volume.

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18

Winzar, Hume. "A Monte-Carlo evaluation of conjoint preference simulators." Thesis, The University of Sydney, 1994. https://hdl.handle.net/2123/27562.

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The purpose of conjoint preference simulators is to translate predicted evaluations in a conjoint analysis study into likelihood of choice (or, more correctly, likelihood of preference). The ease of use of commercially available conjoint software and rating scale techniques could mask some fundamental, and usually flawed, assumptions applications make about evaluation and choice processes. As a result, some researchers could make some costly incorrect decisions based on the results of their conjoint studies.

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19

Mansour, Nabil S. "Inclusion of electron-plasmon interactions in ensemble Monte Carlo simulations of degerate GaAs." Diss., Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/13862.

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20

Loriato, Leandro Amato. "Convertible bond pricing: a Monte Carlo approach." reponame:Repositório Institucional do BNDES, 2014. https://web.bndes.gov.br/bib/jspui/handle/1408/7001.

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Convertible Bonds are interesting hybrid instruments with debt- and equity-like features that have received increasing attention for the last years, especially after the sub-prime mortgage crisis in 2008. This work aims at presenting the main concept behind those instruments, its related features and pricing issues, exhibiting in a constructive manner, from simple products to complex ones, how one may model and price them. To deal with the possibility of American exercises, we implement least-squared and hedged Monte Carlo pricing methods. A clear, flexible, extensible and ready-to-use code implementation for the proposed pricing framework is provided together with some examples of contracts. A discussion of attained numerical results is also presented.
Debêntures Conversíveis são interessantes instrumentos híbridos com características de títulos de dívida e de ações que têm recebido atenção crescente nos últimos anos, especialmente após a crise imobiliária americana em 2008. Esse trabalho tem por objetivo apresentar o conceito principal por trás desses instrumentos, suas características e dificuldades de precificação, exibindo de forma construtiva, de produtos simples a outros mais complexos, como alguém consegue modelar e precificá-los. Para lidar com a possibilidade de exercícios Americanos, implementamos os métodos de precificação de Monte Carlo com mínimos quadrados e com cobertura de risco. Uma implementação clara, flexível, extensível e pronta para uso para o framework de precificação proposto é apresentada com alguns exemplos de contratos. Uma discussão de resultados numéricos encontrados também é apresentada.
Dissertação (mestrado) - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, 2014.

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21

Tse, Wai Tak. "Monte Carlo study on the growth of magnetic ions /." View abstract or full-text, 2007. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202007%20TSE.

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22

Hong, Hee Sun. "Digital nets and sequences for quasi-Monte Carlo methods." HKBU Institutional Repository, 2002. http://repository.hkbu.edu.hk/etd_ra/334.

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23

Anderson, Eric C. "Monte Carlo methods for inference in population genetic models /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/6368.

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24

Mudelsee, Manfred. "Long memory and the aggregation of AR(1) processes." Universitätsbibliothek Leipzig, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-222017.

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Granger (1980) found that the aggregation of m short-memory AR(1) processes yields a long-memory process. Thereby he assumed m -> ∞, Gaussian shape and betadistributed AR(1) parameters over (0; 1). To test hypotheses that long memory in climate time series comes from aggregation, the finding of Granger (1980) cannot be directly applied. First, the number of \"microclimatic\" processes to be aggregated is finite. Second, climatic processes often produce right-skewed data. Third, the AR(1) parameters of the microclimatic processes could be restricted to a narrower interval than (0; 1). We therefore perform Monte Carlo simulations to study aggregation in climate time series under realistic conditions. The long-memory parameter, H, is estimated by fitting an ARFIMA model to various types of aggregations. Our results are as follows. First, for m above a few hundred, H approaches saturation. Second, the distributional shape has little influence, as noted by Granger (1980). Third, the upper limit of the interval for the AR(1) parameter has a strong influence on the saturation value of H, as noted by Granger (1980)
Granger (1980) fand heraus, dass die Summe von m schwach seriell abhängigen AR(1)-Prozessen einen stark seriell abhängigen Prozess ergibt. Er nahm dabei an, dass m -> ∞ geht, die Verteilungen Gaußsch sind und die AR(1)-Parameter beta-verteilt über (0; 1) sind. Um die Hypothese zu testen, daß starke serielle Abhängigkeit in Klimazeitreihen von dieser \"Aggregation\" rührt, kann das Ergebnis von Granger (1980) jedoch nicht direkt angewendet werden. Erstens: die Anzahl \"mikroklimatischer\", zu summierender Prozesse is endlich. Zweitens: Klimaprozesse erzeugen oft rechtsschief verteilte Daten. Drittens: die AR(1)-Parameter der mikroklimatischen Prozesse mögen auf ein engeres Intervall begrenzt sein als (0; 1). Wir f¨uhren deshalb Monte-Carlo-Simulationen durch, um die Aggregation in Klimazeitreihen für realistische Bedingungen zu studieren. Der Parameter H, der die starke serielle Abhängigkeit beschreibt, wird geschätzt durch die Anpassung eines ARFIMA-Modelles an unterschiedliche Aggregations-Typen. Unsere Ergebnisse sind wie folgt. Erstens: für m oberhalb einiger hundert erreicht H S¨attigung. Zweitens: die Verteilungsform hat geringen Einfluß, wie von Granger (1980) bemerkt. Drittens: die obere Grenze des Intervalles für den AR(1)-Parameter hat einen starken Einfluß auf den Sättigungwert von H, wie von Granger (1980) bemerkt

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25

黃柄榕 and Ping-yung Wong. "Molecular clusters on surfaces: a Monte Carlostudy." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31221956.

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Darling, Brian. "A finite element geometry method for Monte Carlo transport calculations." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47016.

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Farmer, Joseph A. "Development of a Quasi-Monte Carlo Method for Thermal Radiation." Thesis, Marquette University, 2019. http://pqdtopen.proquest.com/#viewpdf?dispub=13858322.

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Radiative heat transfer in participating media is among the most challenging computational engineering problems due to the complex nonlinear, nonlocal nature of radiation transport. Many approximate methods have been developed in order to resolve radiative heat transfer in participating media; but approximate methods, by the nature of their approximations, suffer from various shortcomings both in terms of accuracy and robustness. The only methods that can resolve radiative transfer accurately in all configurations are the statistical Monte Carlo-based methods. While the Monte Carlo (MC) method is the most accurate method for resolving radiative heat transfer, it is also notoriously computationally prohibitive in large-scale simulations. To overcome this computational burden, this study details the development of a quasi-Monte Carlo (QMC) method for thermal radiation in participating media with a focus on combustion-related problems. The QMC method employs a low-discrepancy sequence (LDS) in place of the traditional random number sampling mechanism used in Monte Carlo methods to increase computational efficiency. In order to analyze the performance of the QMC method, a systematic comparison of accuracy and computational expense was performed. The QMC method was validated against formal solutions of radiative heat transfer in several one-dimensional configurations and extended to three practical combustion configurations: a turbulent jet flame, a high-pressure industrial gas turbine, and a high-pressure spray combustion chamber. The results from QMC and traditional Monte Carlo are compared against benchmark solutions for each case. It is shown that accuracy of the predicted radiation field from QMC is comparable to MC at lower computational costs. Three different low-discrepancy sequences—Sobol, Halton, and Niederreiter—were examined as part of this work. Finally, recommendations are made in terms of choice of the sequence and the number of the dimensions of the LDS for combustion-relevant configurations. In conclusion, significant improvements in computational costs and accuracy seen in the QMC method makes it a viable alternative to traditional Monte Carlo methods in high-fidelity simulations.

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28

Carraro, Carlo Koonin Steven E. "A path integral Monte Carlo method for the quasielastic response /." Diss., Pasadena, Calif. : California Institute of Technology, 1990. http://resolver.caltech.edu/CaltechETD:etd-06072007-080221.

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VIEIRA, WILSON J. "A General study of undersampling problems in Monte Carlo calculations." reponame:Repositório Institucional do IPEN, 1989. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10258.

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Made available in DSpace on 2014-10-09T12:36:37Z (GMT). No. of bitstreams: 0
Made available in DSpace on 2014-10-09T13:59:11Z (GMT). No. of bitstreams: 1 03975.pdf: 1920852 bytes, checksum: 4a74905dfb7a4bb657984043110cfa4f (MD5)
Tese (Doutoramento)
IPEN/T
University of Tennessee, Knoxville, USA

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30

Rumbe, George Otieno. "Performance evaluation of second price auction using Monte Carlo simulation." Diss., Online access via UMI:, 2007.

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31

Belova, Irina V., Graeme E. Murch, Thomas Fiedler, and Andreas Öchsner. "The lattice Monte Carlo method for solving phenomenological mass and heat transport problems: The lattice Monte Carlo method for solving phenomenological mass andheat transport problems." Diffusion fundamentals 4 (2007) 15, S. 1-23, 2007. https://ul.qucosa.de/id/qucosa%3A14288.

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In this review paper, we introduce the recently developed Lattice Monte Carlo method for addressing and solving phenomenologically-based mass and heat transport problems especially for composite and porous materials. We describe in detail the application of this method to calculate effective mass diffusivities and to determine concentration profiles. Next, we describe in detail the application of this method to the calculation of effective thermal conductivities/thermal diffusivities and the determination of temperature profiles. Where possible, results of the method are compared with exact results or those from application of the Finite Element method. Excellent agreement is demonstrated.

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32

Woo, Sungkwon. "Monte Carlo simulation of labor performance during overtime and its impact on project duration /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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33

Matos, Norman A. Lopez. "Monte Carlo modeling of direct X-ray imaging systems /." Online version of thesis, 2008. http://hdl.handle.net/1850/5745.

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鄒鳳嬌 and Fung-kiu Chow. "Quantum statistical mechanics: a Monte Carlo study of clusters." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31224258.

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Chow, Fung-kiu. "Quantum statistical mechanics a Monte Carlo study of clusters /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22424799.

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36

Blanckenberg, J. P. (Jacobus Petrus). "Monte Carlo simulation of direction sensitive antineutrino detection." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/2885.

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Thesis (MSc (Physics))--University of Stellenbosch, 2010.
ENGLISH ABSTRACT: Neutrino and antineutrino detection is a fairly new eld of experimental physics, mostly due to the small interaction cross section of these particles. Most of the detectors in use today are huge detectors consisting of kilotons of scintilator material and large arrays of photomultiplier tubes. Direction sensitive antineutrino detection has however, not been done (at the time of writing of this thesis). In order to establish the feasibility of direction sensitive antineutrino detection, a Monte Carlo code, DSANDS, was written to simulate the detection process. This code focuses on the neutron and positron (the reaction products after capture on a proton) transport through scintilator media. The results are then used to determine the original direction of the antineutrino, in the same way that data from real detectors would be used, and to compare it with the known direction. Further investigation is also carried out into the required amount of statistics for accurate results in an experimental eld where detection events are rare. Results show very good directional sensitivity of the detection method.
AFRIKAANSE OPSOMMING: Neutrino en antineutrino meting is 'n relatief nuwe veld in eksperimentele sika, hoofsaaklik as gevolg van die klein interaksie deursnee van hierdie deeltjies. Die meeste hedendaagse detektors is massiewe detektors met kilotonne sintilator materiaal en groot aantalle fotovermenigvuldiger buise. Tans is rigting sensitiewe antineutrino metings egter nog nie uit gevoer nie. 'n Monte Carlo kode, DSANDS, is geskryf om die meet proses te simuleer en sodoende die uitvoerbaarheid van rigting sensitiewe antineutrino metings vas te stel. Hierdie kode fokus op die beweging van neutrone en positrone (die reaksie produkte) deur die sintilator medium. Die resultate word dan gebruik om die oorspronklike rigting van die antineutrino te bepaal, soos met data van regte detektors gedoen sou word, en te vergelyk met die bekende oorspronklike rigting van die antineutrino. Verder word daar ook gekyk na die hoeveelheid statistiek wat nodig sal wees om akkurate resultate te kry in 'n veld waar metings baie skaars is. Die resultate wys baie goeie rigting sensitiwiteit van die meet metode.

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37

Ozgur, Soner. "Reduced Complexity Sequential Monte Carlo Algorithms for Blind Receivers." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/10518.

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Monte Carlo algorithms can be used to estimate the state of a system given relative observations. In this dissertation, these algorithms are applied to physical layer communications system models to estimate channel state information, to obtain soft information about transmitted symbols or multiple access interference, or to obtain estimates of all of these by joint estimation. Initially, we develop and analyze a multiple access technique utilizing mutually orthogonal complementary sets (MOCS) of sequences. These codes deliberately introduce inter-chip interference, which is naturally eliminated during processing at the receiver. However, channel impairments can destroy their orthogonality properties and additional processing becomes necessary. We utilize Monte Carlo algorithms to perform joint channel and symbol estimation for systems utilizing MOCS sequences as spreading codes. We apply Rao-Blackwellization to reduce the required number of particles. However, dense signaling constellations, multiuser environments, and the interchannel interference introduced by the spreading codes all increase the dimensionality of the symbol state space significantly. A full maximum likelihood solution is computationally expensive and generally not practical. However, obtaining the optimum solution is critical, and looking at only a part of the symbol space is generally not a good solution. We have sought algorithms that would guarantee that the correct transmitted symbol is considered, while only sampling a portion of the full symbol space. The performance of the proposed method is comparable to the Maximum Likelihood (ML) algorithm. While the computational complexity of ML increases exponentially with the dimensionality of the problem, the complexity of our approach increases only quadratically. Markovian structures such as the one imposed by MOCS spreading sequences can be seen in other physical layer structures as well. We have applied this partitioning approach with some modification to blind equalization of frequency selective fading channel and to multiple-input multiple output receivers that track channel changes. Additionally, we develop a method that obtains a metric for quantifying the convergence rate of Monte Carlo algorithms. Our approach yields an eigenvalue based method that is useful in identifying sources of slow convergence and estimation inaccuracy.

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38

Creal, Drew D. "Essays in sequential Monte Carlo methods for economics and finance /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/7444.

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39

Nobaza, Linda. "Efficient Monte Carlo methods for pricing of electricity derivatives." Thesis, University of the Western Cape, 2012. http://hdl.handle.net/11394/4634.

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>Magister Scientiae - MSc
We discuss efficient Monte Carlo methods for pricing of electricity derivatives. Electricity derivatives are risk management tools used in deregulated electricity markets. In the past,research in electricity derivatives has been dedicated in the modelling of the behaviour of electricity spot prices. Some researchers have used the geometric Brownian motion and the Black Scholes formula to offer a closed-form solution. Electricity spot prices however have unique characteristics such as mean-reverting, non-storability and spikes that render the use of geometric Brownian motion inadequate. Geometric Brownian motion assumes that changes of the underlying asset are continuous and electricity spikes are far from being continuous. Recently there is a greater consensus on the use of Mean-Reverting Jump-Diffusion (MRJD) process to describe the evolution of electricity spot prices. In this thesis,we use Mean-Reverting Jump-Diffusion process to model the evolution of electricity spot prices. Since there is no closed-form technique to price these derivatives when the underlying electricity spot price is assumed to follow MRJD, we use Monte Carlo methods to value electricity forward contracts. We present variance reduction techniques that improve the accuracy of the Monte Carlo Method for pricing electricity derivatives.

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40

Arouna, Bouhari. "Méthodes de Monté Carlo et algorithmes stochastiques." Marne-la-vallée, ENPC, 2004. https://pastel.archives-ouvertes.fr/pastel-00001269.

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41

Gregory, Victor Paul. "Monte Carlo computer simulation of sub-critical Lennard-Jones particles." Thesis, This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-11242009-020125/.

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42

Dubreus, Terrance Maurice. "Monte Carlo simulations for small-world stochastic processes." Diss., Mississippi State : Mississippi State University, 2005. http://library.msstate.edu/content/templates/?a=72.

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43

Li, Xin. "Monte Carlo methods in calculating value at risk." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2148276.

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44

Satterfield, Megan E. "Application of a heterogeneous coarse-mesh transport method (COMET) to radiation therapy problems." Thesis, Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-11192006-213749/.

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45

"Monte Carlo simulation in risk estimation." 2013. http://library.cuhk.edu.hk/record=b5549771.

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本论文主要研究两类风险估计问题：一类是美式期权价格关于模型参数的敏感性估计，另一类是投资组合的风险估计。针对这两类问题，我们相应地提出了高效的蒙特卡洛模拟方法。这构成了本文的两个主要部分。
第二章是本文的第一部分。在这章中，我们将美式期权的敏感性估计问题提成了更具一般性的估计问题：如果一个随机最优化问题依赖于某些模型参数，我们该如何估计其最优目标函数关于参数的敏感性。在该问题中，由于最优决策关于模型参数可能不连续，传统的无穷小扰动分析方法不能直接应用。针对这个困难，我们提出了一种广义的无穷小扰动分析方法，得到敏感性的无偏估计。我们的方法显示, 在估计敏感性时，其实并不需要样本路径关于参数的可微性。这是我们在理论上的新发现。另一方面，该方法可以非常容易的应用于美式期权的敏感性估计。在实际应用中敏感性的无偏估计可以直接嵌入流行的美式期权定价算法，从而同时得到期权价格和价格关于模型参数的敏感性。包括高维问题和多种不同的随机过程模型在内的数值实验，均显示该估计在计算上具有显著的优越性。最后，我们还从理论上刻画了美式期权的近似最优执行策略对敏感性估计的影响，给出了误差上界。
第三章是本文的第二部分。在本章中，我们研究投资组合的风险估计问题。该问题也可被推广成一个一般性的估计问题：如何估计条件期望在作用上一个非线性泛函之后的期望。针对该类估计问题，我们提出了一种多层模拟方法。我们的估计量实际上是一些简单嵌套估计量的线性组合。我们的方法非常容易实现，并且可以被广泛应用于不同的问题结构。理论分析表明我们的方法适用于不同维度的问题并且算法复杂性低于文献中现有的方法。包括低维和高维的数值实验验证了我们的理论分析。
This dissertation mainly consists of two parts: a generalized infinitesimal perturbation analysis (IPA) approach for American option sensitivities estimation and a multilevel Monte Carlo simulation approach for portfolio risk estimation.
In the first part, we develop efficient Monte Carlo methods for estimating American option sensitivities. The problem can be re-formulated as how to perform sensitivity analysis for a stochastic optimization problem when it has model uncertainty. We introduce a generalized IPA approach to resolve the difficulty caused by discontinuity of the optimal decision with respect to the underlying parameter. The unbiased price-sensitivity estimators yielded from this approach demonstrate significant advantages numerically in both high dimensional environments and various process settings. We can easily embed them into many of the most popular pricing algorithms without extra simulation effort to obtain sensitivities as a by-product of the option price. This generalized approach also casts new insights on how to perform sensitivity analysis using IPA: we do not need pathwise differentiability to apply it. Another contribution of this chapter is to investigate how the estimation quality of sensitivities will be affected by the quality of approximated exercise times.
In the second part, we propose a multilevel nested simulation approach to estimate the expectation of a nonlinear function of a conditional expectation, which has a direct application in portfolio risk estimation problems under various risk measures. Our estimator consists of a linear combination of several standard nested estimators. It is very simple to implement and universally applicable across various problem settings. The results of theoretical analysis show that the algorithmic complexities of our estimators are independent of the problem dimensionality and are better than other alternatives in the literature. Numerical experiments, in both low and high dimensional settings, verify our theoretical analysis.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Liu, Yanchu.
"December 2012."
Thesis (Ph.D.)--Chinese University of Hong Kong, 2013.
Includes bibliographical references (leaves 89-96).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstract also in Chinese.
Abstract --- p.i
Abstract in Chinese --- p.iii
Acknowledgements --- p.v
Contents --- p.vii
List of Tables --- p.ix
List of Figures --- p.xii
Chapter 1. --- Overview --- p.1
Chapter 2. --- American Option Sensitivities Estimation via a Generalized IPA Approach --- p.4
Chapter 2.1. --- Introduction --- p.4
Chapter 2.2. --- Formulation of the American Option Pricing Problem --- p.10
Chapter 2.3. --- Main Results --- p.14
Chapter 2.3.1. --- A Generalized IPA Approach in the Presence of a Decision Variable --- p.16
Chapter 2.3.2. --- Unbiased First-Order Sensitivity Estimators --- p.21
Chapter 2.4. --- Implementation Issues and Error Analysis --- p.23
Chapter 2.5. --- Numerical Results --- p.26
Chapter 2.5.1. --- Effects of Dimensionality --- p.27
Chapter 2.5.2. --- Performance under Various Underlying Processes --- p.29
Chapter 2.5.3. --- Effects of Exercising Policies --- p.31
Chapter 2.6. --- Conclusion Remarks and Future Work --- p.33
Chapter 2.7. --- Appendix --- p.35
Chapter 2.7.1. --- Proofs of the Main Results --- p.35
Chapter 2.7.2. --- Likelihood Ratio Estimators --- p.43
Chapter 2.7.3. --- Derivation of Example 2.3 --- p.49
Chapter 3. --- Multilevel Monte Carlo Nested Simulation for Risk Estimation --- p.52
Chapter 3.1. --- Introduction --- p.52
Chapter 3.1.1. --- Examples --- p.53
Risk Measurement of Financial Portfolios --- p.53
Derivatives Pricing --- p.55
Partial Expected Value of Perfect Information --- p.56
Chapter 3.1.2. --- A Standard Nested Estimator --- p.57
Chapter 3.1.3. --- Literature Review --- p.59
Chapter 3.1.4. --- Summary of Our Contributions --- p.61
Chapter 3.2. --- The Multilevel Approach --- p.63
Chapter 3.2.1. --- Motivation --- p.63
Chapter 3.2.2. --- Multilevel Construction --- p.65
Chapter 3.2.3. --- Theoretical Analysis --- p.67
Chapter 3.2.4. --- Further Improvement by Extrapolation --- p.69
Chapter 3.3. --- Numerical Experiments --- p.72
Chapter 3.3.1. --- Single Asset Setting --- p.73
Chapter 3.3.2. --- Multiple Asset Setting --- p.74
Chapter 3.4. --- Concluding Remarks --- p.77
Chapter 3.5. --- Appendix: Technical Assumptions and Proofs of the Main Results --- p.79
Bibliography --- p.89

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46

"Monte Carlo integration." Chinese University of Hong Kong, 1993. http://library.cuhk.edu.hk/record=b5895772.

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by Sze Tsz-leung.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1993.
Includes bibliographical references (leaves 91).
Chapter Chapter 1 --- Introduction
Chapter 1.1 --- Basic concepts of Monte Carlo integration --- p.1
Chapter 1.1.1 --- Importance sampling --- p.4
Chapter 1.1.2 --- Control variate --- p.5
Chapter 1.1.3 --- Antithetic variate --- p.6
Chapter 1.1.4 --- Stratified sampling --- p.7
Chapter 1.1.5 --- Biased Estimator --- p.10
Chapter 1.2 --- Some special methods in Monte Carlo integration --- p.11
Chapter 1.2.1 --- Haber´ةs modified Monte Carlo quadrature I --- p.11
Chapter 1.2.2 --- Haber's modified Monte Carlo quadrature II --- p.11
Chapter 1.2.3 --- Weighted Monte Carlo integration --- p.12
Chapter 1.2.4 --- Adaptive importance sampling --- p.13
Chapter Chapter 2 --- New methods
Chapter 2.1 --- The use of Newton Cotes quadrature formulae in stage one --- p.17
Chapter 2.1.1 --- Using one-dimensional trapezoidal rule --- p.17
Chapter 2.1.2 --- Using two-dimensional or higher dimensional product trapezoidal rule --- p.21
Chapter 2.1.3 --- Extension to higher order one-dimensional Newton Cotes formulae --- p.32
Chapter 2.2 --- The use of Guass quadrature rule in stage one --- p.45
Chapter 2.3 --- Some variations of the new methods --- p.56
Chapter 2.3.1 --- Using probability points in both stages --- p.56
Chapter 2.3.2 --- Importance sampling --- p.59
Chapter 2.3.2.1 --- Triangular distribution --- p.60
Chapter 2.3.2.2 --- Beta distribution --- p.64
Chapter Chapter 3 --- Examples
Chapter 3.1 --- Example one: using trapezoidal rule as basic rule --- p.73
Chapter 3.1.1 --- One-dimensional case --- p.73
Chapter 3.1.2 --- Two-dimensional case --- p.80
Chapter 3.2 --- Example two: Using Simpson's 3/8 rule as basic rule --- p.85
Chapter 3.3 --- Example three： Using Guass rule as basic rule --- p.86
Chapter Chapter 4 --- Conclusion and discussions --- p.88
Reference --- p.91

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47

"Monte Carlo Method for financial derivatives valuation." Thesis, 2002. http://library.cuhk.edu.hk/record=b6073934.

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As for the Monte Carlo Method, we first introduce a brief history of the method and pricing options by using the method. Secondly, the basic idea of using the method in computing option price is described. Thirdly, pricing vanilla options is introduced. Fourthly, we discuss some techniques of improving computing accuracy. They include antithetic variables, control variate methods and importance sampling.
Fifth, we study in detail pricing option problems by using the Monte Carlo method. Then we present a new method on pricing American option, by which, the required memory in computation can be significantly reduced. For most methods of pricing American options, bias exists. However, by using the memory reduction method, minimizing biases is possible. We also discuss the problem for valuation of multiasset options by using our method. In fact, this is an important application of the Monte Carlo method in practical financial problems.
Finally, comparisons of the performances of these numerical results are presented.
Some basic concepts on options are first introduced. Then general methods for pricing options are described. These methods include: analytical formula, finite difference methods and binomial and multinomial methods. These prepare us for the in-depth study on the Monte Carlo method in subsequent chapters.
The Monte Carlo approach has proved to be a valuable and flexible computational tool in modern finance. The Monte Carlo method is the main topic of the thesis.
by Chen Yong.
"August 2002."
Adviser: Raymond Chan.
Source: Dissertation Abstracts International, Volume: 63-10, Section: B, page: 4710.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2002.
Includes bibliographical references (p. 77-79).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts in English and Chinese.
School code: 1307.

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48

Aggarwal, Vikram Srinivasan Ashok. "Improving Monte Carlo linear solvers through better iterative processes." 2004. http://etd.lib.fsu.edu/theses/etd-07132004-065555.

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Thesis (M.S.)--Florida State University, 2004.
Advisor: Dr. Ashok Srinivasan, Florida State University, College of Arts and Sciences, Dept. of Computer Science. Title and description from dissertation home page (viewed Oct. 27, 2004). Includes bibliographical references.

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49

Kuen-Chang, Tsai. "Pricing Exotic Options with the Monte Carlo Method." 2006. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0009-1207200615292400.

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50

"Pricing American-style options by Monte Carlo method." 2002. http://library.cuhk.edu.hk/record=b5891097.

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Abstract:

by Wong Chi Yan.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.
Includes bibliographical references (leaves 38-39).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Introduction --- p.1
Chapter 1.2 --- Monte Carlo Method --- p.2
Chapter 1.3 --- Outline of Thesis --- p.5
Chapter 2 --- The Random Number Generators --- p.7
Chapter 2.1 --- Built-in Random Number Generating Functions --- p.7
Chapter 2.2 --- Linear Congruential Generators --- p.8
Chapter 3 --- Memory Reduction Methods --- p.10
Chapter 3.1 --- The Full-Storage Method --- p.10
Chapter 3.2 --- The Forward-Path Method --- p.12
Chapter 3.3 --- The Backward-Path Method --- p.14
Chapter 4 --- The Least-Squares Method --- p.17
Chapter 5 --- Numerical Examples --- p.28
Chapter 6 --- Concluding Remarks --- p.34
Appendix --- p.36
Bibliography --- p.38

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