Relevant bibliographies by topics / Milstein approximation

Academic literature on the topic 'Milstein approximation'

Author: Grafiati
Published: 10 December 2022
Last updated: 29 January 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Contents

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Milstein approximation.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Milstein approximation"

1

Pieschner, Susanne, and Christiane Fuchs. "Bayesian inference for diffusion processes: using higher-order approximations for transition densities." Royal Society Open Science 7, no. 10 (October 2020): 200270. http://dx.doi.org/10.1098/rsos.200270.

Full text
Abstract:
Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods that introduce auxiliary data. These methods typically approximate the transition densities of the process numerically, both for calculating the posterior densities and proposing auxiliary data. Here, the Euler–Maruyama scheme is the standard approximation technique. However, the MCMC method is computationally expensive. Using higher-order approximations may accelerate it, but the specific implementation and benefit remain unclear. Hence, we investigate the utilization and usefulness of higher-order approximations in the example of the Milstein scheme. Our study demonstrates that the MCMC methods based on the Milstein approximation yield good estimation results. However, they are computationally more expensive and can be applied to multidimensional processes only with impractical restrictions. Moreover, the combination of the Milstein approximation and the well-known modified bridge proposal introduces additional numerical challenges.
APA, Harvard, Vancouver, ISO, and other styles
2

Sengul, Suleyman, Zafer Bekiryazici, and Mehmet Merdan. "Wong-Zakai method for stochastic differential equations in engineering." Thermal Science 25, Spec. issue 1 (2021): 131–42. http://dx.doi.org/10.2298/tsci200528014s.

Full text
Abstract:
In this paper, Wong-Zakai approximation methods are presented for some stochastic differential equations in engineering sciences. Wong-Zakai approximate solutions of the equations are analyzed and the numerical results are compared with results from popular approximation schemes for stochastic differential equations such as Euler-Maruyama and Milstein methods. Several differential equations from engineering problems containing stochastic noise are investigated as numerical examples. Results show that Wong-Zakai method is a reliable tool for studying stochastic differential equations and can be used as an alternative for the known approximation techniques for stochastic models.
APA, Harvard, Vancouver, ISO, and other styles
3

Azadfar, Hamed, and Parisa Nabati. "New truncated Milstein approximation of solution of stochastic differential equations." Communications on Advanced Computational Science with Applications 2018, no. 1 (2018): 15–25. http://dx.doi.org/10.5899/2018/cacsa-00090.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Park, Hail. "Estimation of affine term structure models under the Milstein approximation." Applied Economics Letters 21, no. 9 (March 5, 2014): 651–56. http://dx.doi.org/10.1080/13504851.2014.881962.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Ghayebi, B., and S. M. Hosseini. "A Simplified Milstein Scheme for SPDEs with Multiplicative Noise." Abstract and Applied Analysis 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/140849.

Full text
Abstract:
This paper deals with a research question raised by Jentzen and Röckner (A Milstein scheme for SPDEs, arXiv:1001.2751v4 (2012)), whether the exponential term in their introduced scheme can be replaced by a simpler mollifier. This replacement can lead to more simplification and computational reduction in simulation. So, in this paper, we essentially replace the exponential term with a Padé approximation of order 1 and denote the resulting scheme by simplified Milstein scheme. The convergence analysis for this scheme is carried out and it is shown that even with this replacement the order of convergence is maintained, while the resulting scheme is easier to implement and slightly more efficient computationally. Some numerical tests are given that confirm the order of accuracy and also computational cost reduction.
APA, Harvard, Vancouver, ISO, and other styles
6

Ranjbar, Hassan, Leila Torkzadeh, Dumitru Baleanu, and Kazem Nouri. "Simulating systems of Itô SDEs with split-step $ (\alpha, \beta) $-Milstein scheme." AIMS Mathematics 8, no. 2 (2022): 2576–90. http://dx.doi.org/10.3934/math.2023133.

Full text
Abstract:
<abstract><p>In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step $ (\alpha, \beta) $-Milstein scheme strongly convergence to the exact solution with order $ 1.0 $ in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters $ \alpha, \beta $. Finally, numerical examples illustrate the effectiveness of the theoretical results.</p></abstract>
APA, Harvard, Vancouver, ISO, and other styles
7

Slassi, Mehdi. "A Milstein-based free knot spline approximation for stochastic differential equations." Journal of Complexity 28, no. 1 (February 2012): 37–47. http://dx.doi.org/10.1016/j.jco.2011.03.005.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Mrázek, Milan, and Jan Pospíšil. "Calibration and simulation of Heston model." Open Mathematics 15, no. 1 (May 23, 2017): 679–704. http://dx.doi.org/10.1515/math-2017-0058.

Full text
Abstract:
Abstract We calibrate Heston stochastic volatility model to real market data using several optimization techniques. We compare both global and local optimizers for different weights showing remarkable differences even for data (DAX options) from two consecutive days. We provide a novel calibration procedure that incorporates the usage of approximation formula and outperforms significantly other existing calibration methods. We test and compare several simulation schemes using the parameters obtained by calibration to real market data. Next to the known schemes (log-Euler, Milstein, QE, Exact scheme, IJK) we introduce also a new method combining the Exact approach and Milstein (E+M) scheme. Test is carried out by pricing European call options by Monte Carlo method. Presented comparisons give an empirical evidence and recommendations what methods should and should not be used and why. We further improve the QE scheme by adapting the antithetic variates technique for variance reduction.
APA, Harvard, Vancouver, ISO, and other styles
9

Koulis, Theodoro, Alexander Paseka, and Aerambamoorthy Thavaneswaran. "Recursive Estimation for Continuous Time Stochastic Volatility Models Using the Milstein Approximation." Journal of Mathematical Finance 03, no. 03 (2013): 357–65. http://dx.doi.org/10.4236/jmf.2013.33036.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Barth, Andrea, and Annika Lang. "Milstein Approximation for Advection-Diffusion Equations Driven by Multiplicative Noncontinuous Martingale Noises." Applied Mathematics & Optimization 66, no. 3 (August 10, 2012): 387–413. http://dx.doi.org/10.1007/s00245-012-9176-y.

Full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Milstein approximation"

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.

Full text
Abstract:
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.
APA, Harvard, Vancouver, ISO, and other styles
2

Yuan, Di. "Essays on continuous time diffusion models." Thesis, 2013. http://hdl.handle.net/2440/83807.

Full text
Abstract:
During the past few decades, continuous time diffusion models have become an integral part of financial economics. Especially, in certain core areas in finance, such as interest rate, asset pricing, option pricing, portfolio selection and volatility modelling, continuous time diffusion models have proved to be a very attractive way to conduct research and gain economic intuition. This thesis makes three main contributions to the field of continuous time diffusion models. First, we propose regime-switching Heston, GARCH, and CEV stochastic volatility models where all parameters are allowed to vary depending on the state of the economy. Then we apply these models to describe the dynamics of S&P 500 and VIX. We find strong evidence of regime shifts for all models. The CEV model is statistically preferred to other two nested models in explaining dynamics of data. Second, because the true transition density functions of regime-switching stochastic volatility models are unknown, the standard maximum likelihood estimation cannot be conducted. We first conduct the maximum likelihood estimation with closed-form likelihood expansions for regime-switching continuous time stochastic volatility models. Third, to approximate a continuous time diffusion process, researchers often use the Euler approximation in the literature. Theoretically, the smaller the discretization interval is, the more accurate the Euler approximation is expected to be. However, even when the discretization interval is too small, the accuracy of the Euler approximation can get worse because of the roundoff error and random number generator bias. A variety of univariate and multivariate diffusion models from the literature are considered. We use the solution of a diffusion process when it is available and usable as a benchmark. The Milstein approximation is also adopted to compare the accuracy of the Euler approximation. Depending on the problem of interest, different criteria are used to measure accuracy of approximation. The percentage error and strong convergence can be examined when a good approximation of sample path of a diffusion model is required. The weak convergence is preferred for the cases where approximation of moments of the process matters. In our Monte Carlo simulation studies of diverse diffusion models, we measure accuracy of the Euler approximation not only by using those criteria but also by looking at end point of the approximation. The simulation results show that an appropriate discretization interval must be picked for different diffusion models when applying the Euler approximation.
Thesis (Ph.D.) -- University of Adelaide, School of Economics, 2013
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Milstein approximation"

1

Kuznetsov, Dmitriy F., and Mikhail D. Kuznetsov. "Mean-Square Approximation of Iterated Stochastic Integrals from Strong Exponential Milstein and Wagner-Platen Methods for Non-commutative Semilinear SPDEs Based on Multiple Fourier-Legendre Series." In Recent Developments in Stochastic Methods and Applications, 17–32. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-83266-7_2.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Milstein approximation"

1

Jasim, Abdulghafoor, and Ali Asmael. "Studying Some Stochastic Differential Equations with trigonometric terms with Application." In 3rd International Conference of Mathematics and its Applications. Salahaddin University-Erbil, 2020. http://dx.doi.org/10.31972/ticma22.13.

Full text
Abstract:
In this paper we look at several (trigonometric) stochastic differential equations , we find the general form for such nonlinear stochastic differential equation by using the I'to formula. Then we find the exact solution for the different trigonometric stochastic differential equations by the use of stochastic integrals. Ilustrate the approach with various examples. (precise solution using the Ito integral formula) and approximate solution (numerical approximation (the Euler-Maruyama technique and the Milstein method) were compared to the exact solutions with the error of those approaches.
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Milstein approximation' for particular source types:
Journal articles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography