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Pricing Study on Two Kinds of Power Options in Jump-Diffusion Models with Fractional Brownian Motion and Stochastic Rate
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作者 Jin Li Kaili Xiang Chuanyi Luo 《Applied Mathematics》 2014年第16期2426-2441,共16页
In this paper, under the assumption that the exchange rate follows the extended Vasicek model, the pricing of the reset option in FBM model is investigated. Some interesting themes such as closed-form formulas for the... In this paper, under the assumption that the exchange rate follows the extended Vasicek model, the pricing of the reset option in FBM model is investigated. Some interesting themes such as closed-form formulas for the reset option with a single reset date and the phenomena of delta of the reset jumps existing in the reset option during the reset date are discussed. The closed-form formulae of pricing for two kinds of power options are derived in the end. 展开更多
关键词 STOCHASTIC RATE fractional JUMP-DIFFUSION Process fractional brown motion Power OPTION
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POLYNOMIAL MODEL BASED FAST FRACTIONAL PIXEL SEARCH ALGORITHM FOR H.264/AVC 被引量:3
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作者 Xi Yinglai Hao Chongyang Lai Changcai 《Journal of Electronics(China)》 2006年第6期873-876,共4页
This paper proposed a novel fast fractional pixel search algorithm based on polynomial model. With the analysis of distribution characteristics of motion compensation error surface inside tractional pixel searching wi... This paper proposed a novel fast fractional pixel search algorithm based on polynomial model. With the analysis of distribution characteristics of motion compensation error surface inside tractional pixel searching window, the matching error is fitted with parabola along horizontal and vertical direction respectively. The proposcd searching strategy needs to check only 6 points rather than 16 or 24 points, which are used in the l lierarchical Fractional Pel Search algorithm (HFPS) for 1/4-pel and 1/8-pel Motion Estimation (ME). The experimental results show that the proposed algorithm shows very good capability in keeping the rate distortion performance while reduces computation load to a large extent compared with HFPS algorithm. 展开更多
关键词 motion Estimation (ME) fractional pixel Polynomial model
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A method for simulating sediment incipient motion varying with time and space in an ocean model(FVCOM):development and validation 被引量:2
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作者 ZHU Zichen WANG Yongzhi +3 位作者 BIAN Shuhua HU Zejian LIU Jianqiang LIU Lejun 《Journal of Oceanology and Limnology》 SCIE CAS CSCD 2018年第4期1216-1235,共20页
We modified the sediment incipient motion in a numerical model and evaluated the impact of this modification using a study case of the coastal area around Weihai, China. The modified and unmodified versions of the mod... We modified the sediment incipient motion in a numerical model and evaluated the impact of this modification using a study case of the coastal area around Weihai, China. The modified and unmodified versions of the model were validated by comparing simulated and observed data of currents, waves, and suspended sediment concentrations(SSC) measured from July 25^(th) to July 26^(th), 2006. A fitted Shields diagram was introduced into the sediment model so that the critical erosional shear stress could vary with time. Thus, the simulated SSC patterns were improved to more closely reflect the observed values, so that the relative error of the variation range decreased by up to 34.5% and the relative error of simulated temporally averaged SSC decreased by up to 36%. In the modified model, the critical shear stress values of the simulated silt with a diameter of 0.035 mm and mud with a diameter of 0.004 mm varied from 0.05 to 0.13 N/m^2, and from 0.05 to 0.14 N/m^2, respectively, instead of remaining constant in the unmodified model. Besides, a method of applying spatially varying fractions of the mixed grain size sediment improved the simulated SSC distribution to fit better to the remote sensing map and reproduced the zonal area with high SSC between Heini Bay and the erosion groove in the modified model. The Relative Mean Absolute Error was reduced by between 6% and 79%, depending on the regional attributes when we used the modified method to simulate incipient sediment motion. But the modification achieved the higher accuracy in this study at a cost of computation speed decreasing by 1.52%. 展开更多
关键词 sediment model incipient motion suspended load critical shear stress for erosion fraction of mixed grain size sediment
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ARMA–GARCH model with fractional generalized hyperbolic innovations 被引量:1
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作者 Sung Ik Kim 《Financial Innovation》 2022年第1期1407-1431,共25页
In this study,a multivariate ARMA–GARCH model with fractional generalized hyperbolic innovations exhibiting fat-tail,volatility clustering,and long-range dependence properties is introduced.To define the fractional g... In this study,a multivariate ARMA–GARCH model with fractional generalized hyperbolic innovations exhibiting fat-tail,volatility clustering,and long-range dependence properties is introduced.To define the fractional generalized hyperbolic process,the non-fractional variant is derived by subordinating time-changed Brownian motion to the generalized inverse Gaussian process,and thereafter,the fractional generalized hyperbolic process is obtained using the Volterra kernel.Based on the ARMA–GARCH model with standard normal innovations,the parameters are estimated for the high-frequency returns of six U.S.stocks.Subsequently,the residuals extracted from the estimated ARMA–GARCH parameters are fitted to the fractional and non-fractional generalized hyperbolic processes.The results show that the fractional generalized hyperbolic process performs better in describing the behavior of the residual process of high-frequency returns than the non-fractional processes considered in this study. 展开更多
关键词 Generalized hyperbolic process Time-changed brownian motion Long-range dependence fractional brownian motion ARMA-GARCH model
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On discrete time hedging errors in a fractional Black-Scholes model
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作者 WANG Wen-sheng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2017年第2期211-224,共14页
In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging e... In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging. 展开更多
关键词 discrete time hedging Wick-Itö-Skorohod integral rate of convergence weak convergence incomplete market fractional brownian motion replicate Black-Scholes model
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Pricing Perpetual American Put Option in theMixed Fractional Brownian Motion
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《数学计算(中英文版)》 2015年第2期41-45,共5页
Under the assumption of the underlying asset is driven by the mixed fractional Brownian motion, we obtain the mixed fractionalBlack-Scholes partial differential equation by fractional Ito formula, and the pricing form... Under the assumption of the underlying asset is driven by the mixed fractional Brownian motion, we obtain the mixed fractionalBlack-Scholes partial differential equation by fractional Ito formula, and the pricing formula of perpetual American put option bythis partial differential equation theory. 展开更多
关键词 MIXED fractional brownIAN motion Perpetual American Put OPTION MIXED fractional BLACK-SCHOLES model OPTION PRICING
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A Stock Pricing Model Based on Arithmetic Brown Motion 被引量:1
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作者 YAN Yong-xin, HAN Wen-xiu School of Management, Tianjin University, Tianjin 300072, China 《Journal of Systems Science and Systems Engineering》 SCIE EI CSCD 2001年第3期339-342,共4页
This paper presents a new stock pricing model based on arithmetic Brown motion. The model overcomes the shortcomings of Gordon model completely. With the model investors can estimate the stock value of surplus compani... This paper presents a new stock pricing model based on arithmetic Brown motion. The model overcomes the shortcomings of Gordon model completely. With the model investors can estimate the stock value of surplus companies, deficit companies, zero increase companies and bankrupt companies in long term investment or in short term investment. 展开更多
关键词 stock pricing model arithmetic brown motion Gordon model geometric brown motion.
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Strong Local Non-Determinism of Sub-Fractional Brownian Motion 被引量:1
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作者 Nana Luan 《Applied Mathematics》 2015年第13期2211-2216,共6页
Let be a subfractional Brownian motion in . We prove that is strongly locally nondeterministic.
关键词 Sub-fractional brownIAN motion fractional brownIAN motion self-similar Gaussian Processes STRONG LOCAL NON-DETERMINISM
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Simulation of a Daily Precipitation Time Series Using a Stochastic Model with Filtering
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作者 Chieko Gomi Yasuhisa Kuzuha 《Open Journal of Modern Hydrology》 2013年第4期206-213,共8页
After we modified raw data for anomalies, we conducted spectral analysis using the data. In the frequency, the spectrum is best described by a decaying exponential function. For this reason, stochastic models characte... After we modified raw data for anomalies, we conducted spectral analysis using the data. In the frequency, the spectrum is best described by a decaying exponential function. For this reason, stochastic models characterized by a spectrum attenuated according to a power law cannot be used to model precipitation anomaly. We introduced a new model, the e-model, which properly reproduces the spectrum of the precipitation anomaly. After using the data to infer the parameter values of the e-model, we used the e-model to generate synthetic daily precipitation time series. Comparison with recorded data shows a good agreement. This e-model resembles fractional Brown motion (fBm)/fractional Lévy motion (fLm), especially the spectral method. That is, we transform white noise Xt to the precipitation daily time series. Our analyses show that the frequency of extreme precipitation events is best described by a Lévy law and cannot be accounted with a Gaussian distribution. 展开更多
关键词 E-model Daily Precipitation Time Series FILTERING fractional brownIAN motion fractional Lévy motion Stochastic model
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Critical Exercise Price for American Floating Strike Lookback Option in a Mixed Jump-Diffusion Model 被引量:4
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作者 YANG Zhao-qiang 《Chinese Quarterly Journal of Mathematics》 2018年第3期240-259,共20页
This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using It formula and Wick-It-Skorohod integral, a new market pricing model estab... This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using It formula and Wick-It-Skorohod integral, a new market pricing model established under the environment of mixed jumpdiffusion fractional Brownian motion. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given, then the American floating strike lookback options factorization formula is obtained, the results is generalized the classical Black-Scholes market pricing model. 展开更多
关键词 MIXED JUMP-DIFFUSION fractional brownIAN motion Wick-Ito-Skorohod integral market pricing model option factorization CRITICAL exercise price
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Web software reliability modeling with random impulsive shocks 被引量:1
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作者 Jianfeng Yang Ming Zhao Wensheng Hu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第2期349-356,共8页
As the web-server based business is rapidly developed and popularized, how to evaluate and improve the reliability of web-servers has been extremely important. Although a large num- ber of software reliability growth ... As the web-server based business is rapidly developed and popularized, how to evaluate and improve the reliability of web-servers has been extremely important. Although a large num- ber of software reliability growth models (SRGMs), including those combined with multiple change-points (CPs), have been available, these conventional SRGMs cannot be directly applied to web soft- ware reliability analysis because of the complex web operational profile. To characterize the web operational profile precisely, it should be realized that the workload of a web server is normally non-homogeneous and often observed with the pattern of random impulsive shocks. A web software reliability model with random im- pulsive shocks and its statistical analysis method are developed. In the proposed model, the web server workload is characterized by a geometric Brownian motion process. Based on a real data set from IIS server logs of ICRMS website (www.icrms.cn), the proposed model is demonstrated to be powerful for estimating impulsive shocks and web software reliability. 展开更多
关键词 web software software reliability growth model(SRGM) change-point (CP) impulsive shocks geometric brown-ian motion.
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On a fractional stochastic Hodgkin-Huxley model
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作者 Laure Coutin Jean-Marc Guglielmi Nicolas Marie 《International Journal of Biomathematics》 SCIE 2018年第5期1-16,共16页
The model studied in this paper is a stochastic extension of the so-called neuron model introduced by Hodgkin and Huxley. In the sense of rough paths, the model is perturbed by a multiplicative noise driven by a fract... The model studied in this paper is a stochastic extension of the so-called neuron model introduced by Hodgkin and Huxley. In the sense of rough paths, the model is perturbed by a multiplicative noise driven by a fractional Brownian motion, with a vector field satisfying the viability condition of Coutin and Marie for R× [0, 1]3. An application to the modeling of the membrane potential of nerve fibers damaged by a neuropathy is provided. 展开更多
关键词 Hodgkin-Huxley model stochastic differential equations fractional brownian motion viability theorem.
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Asymptotic behavior for bi-fractional regression models via Malliavin calculus
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作者 Guangjun SHEN Litan YAN 《Frontiers of Mathematics in China》 SCIE CSCD 2014年第1期151-179,共29页
Let B^H1,K1 and BH2,K2 be two independent bi-fractional Brownian motions. In this paper, as a natural extension to the fractional regression model, we consider the asymptotic behavior of the sequence Sn:=∑i=0^n-1K... Let B^H1,K1 and BH2,K2 be two independent bi-fractional Brownian motions. In this paper, as a natural extension to the fractional regression model, we consider the asymptotic behavior of the sequence Sn:=∑i=0^n-1K(n^αBi^H,K1)(Bi+1^H2,K2-Bi^H2,K2)where K is a standard Gaussian kernel function and the bandwidth parameter α satisfies certain hypotheses. We show that its limiting distribution is a mixed normal law involving the local time of the bi-fractional Brownian motion B^H1,K1. We also give the stable convergence of the sequence Sn by using the techniques of the Malliavin calculus. 展开更多
关键词 Bi-fractional brownian motion (bi-fBm) Malliavin calculus regression model
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Pricing of Defaultable Securities Associated with Recovery Rate Under the Stochastic Interest Rate Driven by Fractional Brownian Motion
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作者 ZHOU Qing WANG Qian WU Weixing 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2019年第2期657-680,共24页
This paper considers an improved model of pricing defaultable bonds under the assumption that the interest rate satisfies the Vasicek model driven by fractional Brownian motion(fBm for short)based on the counterparty ... This paper considers an improved model of pricing defaultable bonds under the assumption that the interest rate satisfies the Vasicek model driven by fractional Brownian motion(fBm for short)based on the counterparty risk framework of Jarrow and Yu(2001). The authors use the theory of stochastic analysis of f Bm to derive pricing formulas for the defaultable bonds and study how the counterparty risk, recovery rate, and the Hurst parameter affect the values of the defaultable bonds.Numerical experiment results are presented to demonstrate the findings. 展开更多
关键词 Counterparty risk defaultable BOND fractional brownIAN motion RECOVERY rate Vasicek model
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分数Brown运动驱动的具有壁附着的恒化器模型的随机吸引子
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作者 李依洋 曾才斌 黄在堂 《广西师范大学学报(自然科学版)》 CAS 北大核心 2023年第5期61-68,共8页
大多数恒化器模型忽略了微生物的壁附着行为,并且对随机生物系统的记忆效应研究较少。基于此,本文研究由分数Brown运动驱动的具有壁附着的恒化器模型的随机吸引子的存在性。首先,引入合适的停时序列,将连续随机动力系统转化为一序列小... 大多数恒化器模型忽略了微生物的壁附着行为,并且对随机生物系统的记忆效应研究较少。基于此,本文研究由分数Brown运动驱动的具有壁附着的恒化器模型的随机吸引子的存在性。首先,引入合适的停时序列,将连续随机动力系统转化为一序列小区间上的离散随机动力系统;然后,在小的闭球内构造随机集,并证明其紧性、缓增性、吸引性,由此证明所生成随机动力系统拉回吸引子的存在性;最后,通过数值分析验证所得理论结果的正确性和有效性。 展开更多
关键词 随机吸引子 分数brown运动 恒化器 壁附着 停时序列 记忆效应
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基于银行间同业拆放利率的长记忆随机利率模型研究 被引量:1
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作者 孙晓霞 王冰 《统计研究》 CSSCI 北大核心 2024年第2期149-160,共12页
研究表明利率序列具有长记忆性,故本文使用分数布朗运动代替经典CIR模型中的几何布朗运动,构建分数CIR模型,并通过欧拉离散对分数CIR过程进行路径模拟。由于分数布朗运动的非马尔可夫性和增量不独立,无法使用极大似然估计和马尔可夫链... 研究表明利率序列具有长记忆性,故本文使用分数布朗运动代替经典CIR模型中的几何布朗运动,构建分数CIR模型,并通过欧拉离散对分数CIR过程进行路径模拟。由于分数布朗运动的非马尔可夫性和增量不独立,无法使用极大似然估计和马尔可夫链蒙特卡洛方法对分数CIR模型进行参数估计,故本文引入间接推断估计法,并通过蒙特卡洛模拟证明该方法的可行性。本文使用间接推断估计法对我国银行间同业拆放利率数据进行实证分析及样本外预测,将经典CIR模型、分数O-U过程、分数CIR模型的拟合轨道与真实轨道进行分析对比,得出分数CIR模型更适用于描述具有长记忆性的利率序列。本文重点研究一种用于分数CIR模型的参数估计方法,未来将继续探究其他参数估计方法并对比这些方法的有效性和稳健性。 展开更多
关键词 长记忆性 分数布朗运动 分数CIR模型 间接推断估计
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混合分数Brownian运动下美式期权定价
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作者 韩婵 孙玉东 《重庆理工大学学报(自然科学)》 CAS 北大核心 2019年第9期229-232,共4页
在混合分数Brownian运动驱动的Black-Scholes模型下,研究了美式期权定价问题。利用自融资策略和财富过程的交易费用,给出了一个结构更简单、使用更灵活的美式看跌期权近似定价公式。
关键词 美式看跌期权 BLACK-SCHOLES模型 混合分数brownian运动 近似定价公式
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分数Brown运动扰动风险模型的破产概率模拟计算 被引量:1
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作者 王琪 薛红 陈毛毛 《计算机工程与应用》 CSCD 北大核心 2020年第8期215-219,共5页
分数Brown运动具有长程相依性,且已被应用于风险理论研究。考虑到现实中保险公司盈余过程序列具有长程相依性,建立分数Brown运动扰动风险模型来刻画盈余过程序列,并对有限时破产概率进行了Monte-Carlo模拟计算。结合Cholesky分解方法模... 分数Brown运动具有长程相依性,且已被应用于风险理论研究。考虑到现实中保险公司盈余过程序列具有长程相依性,建立分数Brown运动扰动风险模型来刻画盈余过程序列,并对有限时破产概率进行了Monte-Carlo模拟计算。结合Cholesky分解方法模拟分数Brown运动样本轨道;提出一种有效的数值模拟算法对有限时破产概率进行了模拟计算,并通过数值算例研究了Hurst指数和波动系数对破产概率的影响;结合中国太平洋财产保险股份有限公司在2008—2017年间的数据进行实证分析,从而根据有限时破产概率的数值模拟结果分析保险公司的运营状况。 展开更多
关键词 长程相依性 分数brown运动 Monte-Carlo模拟计算 破产概率
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具有分数Brown运动的随机时滞Lotka-Volterra模型数值解
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作者 麻硕 张启敏 《西南师范大学学报(自然科学版)》 CAS 北大核心 2016年第1期24-30,共7页
由于带分数Brown运动的随机时滞Lotka-Volterra模型的精确解很难得到,因此数值近似方法成为了求解此方程的有力工具.根据Euler数值方法,利用It公式和分数Brown运动的性质,讨论带分数Brown运动的随机时滞Lotka-Volterra模型数值解的有... 由于带分数Brown运动的随机时滞Lotka-Volterra模型的精确解很难得到,因此数值近似方法成为了求解此方程的有力工具.根据Euler数值方法,利用It公式和分数Brown运动的性质,讨论带分数Brown运动的随机时滞Lotka-Volterra模型数值解的有界性和收敛性,并通过数值算例对给出的数值计算方法进行验证. 展开更多
关键词 随机时滞Lotka-Volterra模型 分数brown运动 数值解 ITO公式
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带标准Brown运动扰动风险模型的破产概率模拟计算
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作者 王琪 薛红 陈毛毛 《四川理工学院学报(自然科学版)》 CAS 2019年第6期82-89,共8页
当索赔额序列服从重尾分布时,带标准Brown运动扰动风险模型的破产概率无解析表达式。首先提出一种模拟带标准Brown运动扰动风险模型盈余轨道的程序思想,结合Monte-Carlo方法,讨论风险模型在有限时间内的破产概率,并通过数值算例验证了... 当索赔额序列服从重尾分布时,带标准Brown运动扰动风险模型的破产概率无解析表达式。首先提出一种模拟带标准Brown运动扰动风险模型盈余轨道的程序思想,结合Monte-Carlo方法,讨论风险模型在有限时间内的破产概率,并通过数值算例验证了程序的有效性。其次根据中国太平洋财产保险股份有限公司2014年和2015年的数据,利用统计分析方法,采用广义Pareto分布刻画重大理赔额序列,Poisson过程刻画理赔次数,标准Brown运动刻画其它风险干扰因素。最后对该公司有限时间内的破产概率进行了Monte-Carlo模拟计算。由于综合考虑了其他营业支出及风险干扰等影响因素,使得保险公司在有限时间内的破产概率模拟计算结果更加贴合实际。 展开更多
关键词 带标准brown运动扰动风险模型 Monte-Carlo数值模拟 有限时间破产概率
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