This study investigates whether the implied crude oil volatility and the historical OPEC price volatility can impact the return to and volatility of the energy-sector equity indices in Iran.The analysis specifically c...This study investigates whether the implied crude oil volatility and the historical OPEC price volatility can impact the return to and volatility of the energy-sector equity indices in Iran.The analysis specifically considers the refining,drilling,and petrochemical equity sectors of the Tehran Stock Exchange.The parameter estimation uses the quasi-Monte Carlo and Bayesian optimization methods in the framework of a generalized autoregressive conditional heteroskedasticity model,and a complementary Bayesian network analysis is also conducted.The analysis takes into account geopolitical risk and economic policy uncertainty data as other proxies for uncertainty.This study also aims to detect different price regimes for each equity index in a novel way using homogeneous/non-homogeneous Markov switching autoregressive models.Although these methods provide improvements by restricting the analysis to a specific price-regime period,they produce conflicting results,rendering it impossible to draw general conclusions regarding the contagion effect on returns or the volatility transmission between markets.Nevertheless,the results indicate that the OPEC(historical)price volatility has a stronger effect on the energy sectors than the implied volatility has.These types of oil price shocks are found to have no effect on the drilling sector price pattern,whereas the refining and petrochemical equity sectors do seem to undergo changes in their price patterns nearly concurrently with future demand shocks and oil supply shocks,respectively,gaining dominance in the oil market.展开更多
Considering the stochastic spatial variation of geotechnical parameters over the slope, a Stochastic Finite Element Method (SFEM) is established based on the combination of the Shear Strength Reduction (SSR) concept a...Considering the stochastic spatial variation of geotechnical parameters over the slope, a Stochastic Finite Element Method (SFEM) is established based on the combination of the Shear Strength Reduction (SSR) concept and quasi-Monte Carlo simulation. The shear strength reduction FEM is superior to the slice method based on the limit equilibrium theory in many ways, so it will be more powerful to assess the reliability of global slope stability when combined with probability theory. To illustrate the performance of the proposed method, it is applied to an example of simple slope. The results of simulation show that the proposed method is effective to perform the reliability analysis of global slope stability without presupposing a potential slip surface.展开更多
In this project, we consider obtaining Fourier features via more efficient sampling schemes to approximate the kernel in LFMs. A latent force model (LFM) is a Gaussian process whose covariance functions follow an Expo...In this project, we consider obtaining Fourier features via more efficient sampling schemes to approximate the kernel in LFMs. A latent force model (LFM) is a Gaussian process whose covariance functions follow an Exponentiated Quadratic (EQ) form, and the solutions for the cross-covariance are expensive due to the computational complexity. To reduce the complexity of mathematical expressions, random Fourier features (RFF) are applied to approximate the EQ kernel. Usually, the random Fourier features are implemented with Monte Carlo sampling, but this project proposes replacing the Monte-Carlo method with the Quasi-Monte Carlo (QMC) method. The first-order and second-order models’ experiment results demonstrate the decrease in NLPD and NMSE, which revealed that the models with QMC approximation have better performance.展开更多
To improve the precisions of pose error analysis for 6-dof parallel kinematic mechanism( PKM)during assembly quality control,a Sobol sequence based on Quasi Monte Carlo( QMC) method is introduced and implemented in po...To improve the precisions of pose error analysis for 6-dof parallel kinematic mechanism( PKM)during assembly quality control,a Sobol sequence based on Quasi Monte Carlo( QMC) method is introduced and implemented in pose accuracy analysis for the PKM in this paper. The Sobol sequence based on Quasi Monte Carlo with the regularity and uniformity of samples in high dimensions,can prevail traditional Monte Carlo method with up to 98. 59% and 98. 25% enhancement for computational precision of pose error statistics.Then a PKM tolerance design system integrating this method is developed and with it pose error distributions of the PKM within a prescribed workspace are finally obtained and analyzed.展开更多
To validate the ability of full configuration interaction quantum Monte Carlo （FCIQMC） for studying the 2D Hubbard model near half-filling regime, the ground state energies of a 4×44×4 square lattice syste...To validate the ability of full configuration interaction quantum Monte Carlo （FCIQMC） for studying the 2D Hubbard model near half-filling regime, the ground state energies of a 4×44×4 square lattice system with various interaction strengths are calculated. It is found that the calculated results are in good agreement with those obtained by exact diagonalization （i.e., the exact values for a given basis set） when the population of psi particles （psips） is higher than the critical population required to correctly sample the ground state wave function. In addition, the variations of the average computational time per 20 Monte Carlo cycles with the coupling strength and the number of processors are also analyzed. The calculated results show that the computational efficiency of an FCIQMC calculation is mainly affected by the total population of psips and the communication between processors. These results can provide useful references for understanding the FCIQMC algorithm, studying the ground state properties of the 2D Hubbard model for the larger system size by the FCIQMC method and using a computational budget as effectively as possible.展开更多
As one of the major methods for the simulation of option pricing,Monte Carlo method assumes random fluctuations in the distribution of asset prices.Under certain uncertainties process,different evolution paths could b...As one of the major methods for the simulation of option pricing,Monte Carlo method assumes random fluctuations in the distribution of asset prices.Under certain uncertainties process,different evolution paths could be simulated so as to finally yield the expectation value of the asset price,which requires a lot of simulations to ensure the accuracy based on huge and expensive calculations.In order to solve the above computational problem,quantum Monte Carlo(QMC)has been established and applied in the relevant systems such as European call options.In this work,both MC and QM methods are adopted to simulate European call options.Based on the preparation of quantum states in QMC algorithm and the construction of quantum circuits by simulating a quantum hardware environment on a traditional computer,the amplitude estimation(AE)algorithm is found to play a secondary role in accelerating the pricing of European options.More importantly,the payoff function and the time required for the simulation in QMC method show some improvements than those in MC method.展开更多
基于可靠度的最优化设计能有效地处理岩土工程中存在的不确定性,在工程界和学界日益得到重视。然而,传统的基于可靠度的分析方法需要进行多次计算并不断重构计算模型,计算量巨大且难以实施。鉴于此,提出一个基于滑移线场理论的概率边坡...基于可靠度的最优化设计能有效地处理岩土工程中存在的不确定性,在工程界和学界日益得到重视。然而,传统的基于可靠度的分析方法需要进行多次计算并不断重构计算模型,计算量巨大且难以实施。鉴于此,提出一个基于滑移线场理论的概率边坡优化设计方法。该方法采用更加高效的拟蒙特卡罗模拟(quasi-Monte Carlo simulation,QMCS)来确定边坡的失效概率,在每次模拟过程中采用滑移线场理论来分析边坡的稳定性。为了更加高效的确定满足目标失效概率的设计坡角,提出一个简单而有效地二分搜索方法。以一个边坡为例设计了不同目标失效概率的坡角,并验证所提方法的有效性。结果表明:所提方法最多只需36.29 min就能得到满足目标失效概率的坡角。所提出的边坡概率优化设计方法避免了计算模型的反复重构,计算效率较好,可为基于可靠度边坡设计提供新的可选手段。展开更多
Monte Carlo and quasi-Monte Carlomethods arewidely used in scientific studies.As quasi-Monte Carlo simulations have advantage over ordinaryMonte Carlomethods,this paper proposes a new quasi-Monte Carlo method to simul...Monte Carlo and quasi-Monte Carlomethods arewidely used in scientific studies.As quasi-Monte Carlo simulations have advantage over ordinaryMonte Carlomethods,this paper proposes a new quasi-Monte Carlo method to simulate Brownian sheet via its Karhunen–Loéve expansion.The proposed new approach allocates quasi-random sequences for the simulation of random components of the Karhunen–Loéve expansion by maximum reducing its variability.We apply the quasi-MonteCarlo approach to an option pricing problem for a class of interest rate models whose instantaneous forward rate driven by a different stochastic shock through Brownian sheet andwe demonstrate the application with an empirical problem.展开更多
Quasi-Monte Carlo methods and stochastic collocation methods based on sparse grids have become popular with solving stochastic partial differential equations.These methods use deterministic points for multi-dimensiona...Quasi-Monte Carlo methods and stochastic collocation methods based on sparse grids have become popular with solving stochastic partial differential equations.These methods use deterministic points for multi-dimensional integration or interpolation without suffering from the curse of dimensionality.It is not evident which method is best,specially on random models of physical phenomena.We numerically study the error of quasi-Monte Carlo and sparse gridmethods in the context of groundwater flow in heterogeneous media.In particular,we consider the dependence of the variance error on the stochastic dimension and the number of samples/collocation points for steady flow problems in which the hydraulic conductivity is a lognormal process.The suitability of each technique is identified in terms of computational cost and error tolerance.展开更多
The generalized likelihood ratio(GLR)method is a recently introduced gradient estimation method for handling discontinuities in a wide range of sample performances.We put the GLR methods from previous work into a sing...The generalized likelihood ratio(GLR)method is a recently introduced gradient estimation method for handling discontinuities in a wide range of sample performances.We put the GLR methods from previous work into a single framework,simplify regularity conditions to justify the unbiasedness of GLR,and relax some of those conditions that are difficult to verify in practice.Moreover,we combine GLR with conditional Monte Carlo methods and randomized quasi-Monte Carlo methods to reduce the variance.Numerical experiments show that variance reduction could be significant in various applications.展开更多
文摘This study investigates whether the implied crude oil volatility and the historical OPEC price volatility can impact the return to and volatility of the energy-sector equity indices in Iran.The analysis specifically considers the refining,drilling,and petrochemical equity sectors of the Tehran Stock Exchange.The parameter estimation uses the quasi-Monte Carlo and Bayesian optimization methods in the framework of a generalized autoregressive conditional heteroskedasticity model,and a complementary Bayesian network analysis is also conducted.The analysis takes into account geopolitical risk and economic policy uncertainty data as other proxies for uncertainty.This study also aims to detect different price regimes for each equity index in a novel way using homogeneous/non-homogeneous Markov switching autoregressive models.Although these methods provide improvements by restricting the analysis to a specific price-regime period,they produce conflicting results,rendering it impossible to draw general conclusions regarding the contagion effect on returns or the volatility transmission between markets.Nevertheless,the results indicate that the OPEC(historical)price volatility has a stronger effect on the energy sectors than the implied volatility has.These types of oil price shocks are found to have no effect on the drilling sector price pattern,whereas the refining and petrochemical equity sectors do seem to undergo changes in their price patterns nearly concurrently with future demand shocks and oil supply shocks,respectively,gaining dominance in the oil market.
文摘Considering the stochastic spatial variation of geotechnical parameters over the slope, a Stochastic Finite Element Method (SFEM) is established based on the combination of the Shear Strength Reduction (SSR) concept and quasi-Monte Carlo simulation. The shear strength reduction FEM is superior to the slice method based on the limit equilibrium theory in many ways, so it will be more powerful to assess the reliability of global slope stability when combined with probability theory. To illustrate the performance of the proposed method, it is applied to an example of simple slope. The results of simulation show that the proposed method is effective to perform the reliability analysis of global slope stability without presupposing a potential slip surface.
文摘In this project, we consider obtaining Fourier features via more efficient sampling schemes to approximate the kernel in LFMs. A latent force model (LFM) is a Gaussian process whose covariance functions follow an Exponentiated Quadratic (EQ) form, and the solutions for the cross-covariance are expensive due to the computational complexity. To reduce the complexity of mathematical expressions, random Fourier features (RFF) are applied to approximate the EQ kernel. Usually, the random Fourier features are implemented with Monte Carlo sampling, but this project proposes replacing the Monte-Carlo method with the Quasi-Monte Carlo (QMC) method. The first-order and second-order models’ experiment results demonstrate the decrease in NLPD and NMSE, which revealed that the models with QMC approximation have better performance.
基金Sponsored by the National Defense Basic Scientific Research Program(Grant No.A0320110019)the Shanghai Science and Technology Innovation Action Plan(Grant No.11DZ1120800)
文摘To improve the precisions of pose error analysis for 6-dof parallel kinematic mechanism( PKM)during assembly quality control,a Sobol sequence based on Quasi Monte Carlo( QMC) method is introduced and implemented in pose accuracy analysis for the PKM in this paper. The Sobol sequence based on Quasi Monte Carlo with the regularity and uniformity of samples in high dimensions,can prevail traditional Monte Carlo method with up to 98. 59% and 98. 25% enhancement for computational precision of pose error statistics.Then a PKM tolerance design system integrating this method is developed and with it pose error distributions of the PKM within a prescribed workspace are finally obtained and analyzed.
基金Supported by the Natural Science Foundation for Colleges and Universities of Jiangsu Province under Grant No 16KJB140008the National Natural Science Foundation of China under Grant Nos 11447204 and 11647164+1 种基金the Natural Science Foundation of Jiangsu Province under Grant No BK20151079the Scientific Research Foundation of Nanjing Xiaozhuang University under Grant No 2015NXY34
文摘To validate the ability of full configuration interaction quantum Monte Carlo （FCIQMC） for studying the 2D Hubbard model near half-filling regime, the ground state energies of a 4×44×4 square lattice system with various interaction strengths are calculated. It is found that the calculated results are in good agreement with those obtained by exact diagonalization （i.e., the exact values for a given basis set） when the population of psi particles （psips） is higher than the critical population required to correctly sample the ground state wave function. In addition, the variations of the average computational time per 20 Monte Carlo cycles with the coupling strength and the number of processors are also analyzed. The calculated results show that the computational efficiency of an FCIQMC calculation is mainly affected by the total population of psips and the communication between processors. These results can provide useful references for understanding the FCIQMC algorithm, studying the ground state properties of the 2D Hubbard model for the larger system size by the FCIQMC method and using a computational budget as effectively as possible.
基金This work was financially supported by the National Natural Science Foundation of China Granted No.11764028。
文摘As one of the major methods for the simulation of option pricing,Monte Carlo method assumes random fluctuations in the distribution of asset prices.Under certain uncertainties process,different evolution paths could be simulated so as to finally yield the expectation value of the asset price,which requires a lot of simulations to ensure the accuracy based on huge and expensive calculations.In order to solve the above computational problem,quantum Monte Carlo(QMC)has been established and applied in the relevant systems such as European call options.In this work,both MC and QM methods are adopted to simulate European call options.Based on the preparation of quantum states in QMC algorithm and the construction of quantum circuits by simulating a quantum hardware environment on a traditional computer,the amplitude estimation(AE)algorithm is found to play a secondary role in accelerating the pricing of European options.More importantly,the payoff function and the time required for the simulation in QMC method show some improvements than those in MC method.
文摘基于可靠度的最优化设计能有效地处理岩土工程中存在的不确定性,在工程界和学界日益得到重视。然而,传统的基于可靠度的分析方法需要进行多次计算并不断重构计算模型,计算量巨大且难以实施。鉴于此,提出一个基于滑移线场理论的概率边坡优化设计方法。该方法采用更加高效的拟蒙特卡罗模拟(quasi-Monte Carlo simulation,QMCS)来确定边坡的失效概率,在每次模拟过程中采用滑移线场理论来分析边坡的稳定性。为了更加高效的确定满足目标失效概率的设计坡角,提出一个简单而有效地二分搜索方法。以一个边坡为例设计了不同目标失效概率的坡角,并验证所提方法的有效性。结果表明:所提方法最多只需36.29 min就能得到满足目标失效概率的坡角。所提出的边坡概率优化设计方法避免了计算模型的反复重构,计算效率较好,可为基于可靠度边坡设计提供新的可选手段。
基金The research of Yazhen Wang was supported in part by NSF[grant number DMS-12-65203][grant number DMS-15-28375].
文摘Monte Carlo and quasi-Monte Carlomethods arewidely used in scientific studies.As quasi-Monte Carlo simulations have advantage over ordinaryMonte Carlomethods,this paper proposes a new quasi-Monte Carlo method to simulate Brownian sheet via its Karhunen–Loéve expansion.The proposed new approach allocates quasi-random sequences for the simulation of random components of the Karhunen–Loéve expansion by maximum reducing its variability.We apply the quasi-MonteCarlo approach to an option pricing problem for a class of interest rate models whose instantaneous forward rate driven by a different stochastic shock through Brownian sheet andwe demonstrate the application with an empirical problem.
文摘Quasi-Monte Carlo methods and stochastic collocation methods based on sparse grids have become popular with solving stochastic partial differential equations.These methods use deterministic points for multi-dimensional integration or interpolation without suffering from the curse of dimensionality.It is not evident which method is best,specially on random models of physical phenomena.We numerically study the error of quasi-Monte Carlo and sparse gridmethods in the context of groundwater flow in heterogeneous media.In particular,we consider the dependence of the variance error on the stochastic dimension and the number of samples/collocation points for steady flow problems in which the hydraulic conductivity is a lognormal process.The suitability of each technique is identified in terms of computational cost and error tolerance.
基金the National Natural Science Foundation of China(NSFC)under Grant 72022001,92146003,71901003the Air Force Office of Scientific Research under Grant FA95502010211by Discover GrantRGPIN-2018-05795fromNSERCCanada.
文摘The generalized likelihood ratio(GLR)method is a recently introduced gradient estimation method for handling discontinuities in a wide range of sample performances.We put the GLR methods from previous work into a single framework,simplify regularity conditions to justify the unbiasedness of GLR,and relax some of those conditions that are difficult to verify in practice.Moreover,we combine GLR with conditional Monte Carlo methods and randomized quasi-Monte Carlo methods to reduce the variance.Numerical experiments show that variance reduction could be significant in various applications.
