The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the po...The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.展开更多
We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
The degree of variation of trading prices with respect to time is volatility-measured by the standard deviation of returns. We present the estimation of stochastic volatility from the stochastic differential equation ...The degree of variation of trading prices with respect to time is volatility-measured by the standard deviation of returns. We present the estimation of stochastic volatility from the stochastic differential equation for evenly spaced data. We indicate that, the price process is driven by a semi-martingale and the data are evenly spaced. The results of Malliavin and Mancino [1] are extended by adding a compensated poisson jump that uses a quadratic variation to calculate volatility. The volatility is computed from a daily data without assuming its functional form. Our result is well suited for financial market applications and in particular the analysis of high frequency data for the computation of volatility.展开更多
Although Geometric Brownian Motion and Jump Diffusion Models have largely dominated the literature on asset price modeling, studies of the empirical stock price data on the Ghana Stock Exchange have led to the conclus...Although Geometric Brownian Motion and Jump Diffusion Models have largely dominated the literature on asset price modeling, studies of the empirical stock price data on the Ghana Stock Exchange have led to the conclusion that there are some stocks in which the return processes consistently depart from these models in theory as well as in its statistical properties. This paper gives a fundamental review of the development of a stock price model based on pure jump processes to capture the unique behavior exhibited by some stocks on the Exchange. Although pure jump processes have been examined thoroughly by other authors, there is a lack of mathematical clarity in terms of deriving the underlying stock price process. This paper provides a link between stock prices existing on a measure space to its development as a pure jump Levy process. We test the suitability of the model to the empirical evidence using numerical procedures. The simulation results show that the trajectories of the model are a better fit for the empirical data than those produced by the diffusion and jump diffusion models.展开更多
Static Poisson’s ratio(vs)is crucial for determining geomechanical properties in petroleum applications,namely sand production.Some models have been used to predict vs;however,the published models were limited to spe...Static Poisson’s ratio(vs)is crucial for determining geomechanical properties in petroleum applications,namely sand production.Some models have been used to predict vs;however,the published models were limited to specific data ranges with an average absolute percentage relative error(AAPRE)of more than 10%.The published gated recurrent unit(GRU)models do not consider trend analysis to show physical behaviors.In this study,we aim to develop a GRU model using trend analysis and three inputs for predicting n s based on a broad range of data,n s(value of 0.1627-0.4492),bulk formation density(RHOB)(0.315-2.994 g/mL),compressional time(DTc)(44.43-186.9 μs/ft),and shear time(DTs)(72.9-341.2μ s/ft).The GRU model was evaluated using different approaches,including statistical error an-alyses.The GRU model showed the proper trends,and the model data ranges were wider than previous ones.The GRU model has the largest correlation coefficient(R)of 0.967 and the lowest AAPRE,average percent relative error(APRE),root mean square error(RMSE),and standard deviation(SD)of 3.228%,1.054%,4.389,and 0.013,respectively,compared to other models.The GRU model has a high accuracy for the different datasets:training,validation,testing,and the whole datasets with R and AAPRE values were 0.981 and 2.601%,0.966 and 3.274%,0.967 and 3.228%,and 0.977 and 2.861%,respectively.The group error analyses of all inputs show that the GRU model has less than 5% AAPRE for all input ranges,which is superior to other models that have different AAPRE values of more than 10% at various ranges of inputs.展开更多
Electron density in fusion plasma is usually diagnosed using laser-aided interferometers. The phase difference signal obtained after phase demodulation is wrapped, which is also called a fringe jump. A method has been...Electron density in fusion plasma is usually diagnosed using laser-aided interferometers. The phase difference signal obtained after phase demodulation is wrapped, which is also called a fringe jump. A method has been developed to unwrap the phase difference signal in real time using FPGA, specifically designed to handle fringe jumps in the hydrogen cyanide(HCN) laser interferometer on the EAST superconducting tokamak. This method is designed for a phase demodulator using the fast Fourier transform(FFT) method at the front end. The method is better adapted for hardware implementation compared to complex mathematical analysis algorithms, such as field programmable gate array(FPGA). It has been applied to process the phase measurement results of the HCN laser interferometer on EAST in real time. Electron density results show good confidence in the fringe jump unwrapping method. Further possible application in other laser interferometers, such as the POlarimeter-INTerferometer(POINT)system on EAST tokamak is also discussed.展开更多
We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavio...We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavior of a solution u near the boundary OD up to the third or higher term.展开更多
基金supported by the National Board for Higher Mathematics,Mumbai,India under Grant No.2/48(5)/2013/NBHM(R.P.)/RD-II/688 dt 16.01.2014
文摘The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.
文摘We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
文摘The degree of variation of trading prices with respect to time is volatility-measured by the standard deviation of returns. We present the estimation of stochastic volatility from the stochastic differential equation for evenly spaced data. We indicate that, the price process is driven by a semi-martingale and the data are evenly spaced. The results of Malliavin and Mancino [1] are extended by adding a compensated poisson jump that uses a quadratic variation to calculate volatility. The volatility is computed from a daily data without assuming its functional form. Our result is well suited for financial market applications and in particular the analysis of high frequency data for the computation of volatility.
文摘Although Geometric Brownian Motion and Jump Diffusion Models have largely dominated the literature on asset price modeling, studies of the empirical stock price data on the Ghana Stock Exchange have led to the conclusion that there are some stocks in which the return processes consistently depart from these models in theory as well as in its statistical properties. This paper gives a fundamental review of the development of a stock price model based on pure jump processes to capture the unique behavior exhibited by some stocks on the Exchange. Although pure jump processes have been examined thoroughly by other authors, there is a lack of mathematical clarity in terms of deriving the underlying stock price process. This paper provides a link between stock prices existing on a measure space to its development as a pure jump Levy process. We test the suitability of the model to the empirical evidence using numerical procedures. The simulation results show that the trajectories of the model are a better fit for the empirical data than those produced by the diffusion and jump diffusion models.
基金The authors thank the Yayasan Universiti Teknologi PETRONAS(YUTP FRG Grant No.015LC0-428)at Universiti Teknologi PETRO-NAS for supporting this study.
文摘Static Poisson’s ratio(vs)is crucial for determining geomechanical properties in petroleum applications,namely sand production.Some models have been used to predict vs;however,the published models were limited to specific data ranges with an average absolute percentage relative error(AAPRE)of more than 10%.The published gated recurrent unit(GRU)models do not consider trend analysis to show physical behaviors.In this study,we aim to develop a GRU model using trend analysis and three inputs for predicting n s based on a broad range of data,n s(value of 0.1627-0.4492),bulk formation density(RHOB)(0.315-2.994 g/mL),compressional time(DTc)(44.43-186.9 μs/ft),and shear time(DTs)(72.9-341.2μ s/ft).The GRU model was evaluated using different approaches,including statistical error an-alyses.The GRU model showed the proper trends,and the model data ranges were wider than previous ones.The GRU model has the largest correlation coefficient(R)of 0.967 and the lowest AAPRE,average percent relative error(APRE),root mean square error(RMSE),and standard deviation(SD)of 3.228%,1.054%,4.389,and 0.013,respectively,compared to other models.The GRU model has a high accuracy for the different datasets:training,validation,testing,and the whole datasets with R and AAPRE values were 0.981 and 2.601%,0.966 and 3.274%,0.967 and 3.228%,and 0.977 and 2.861%,respectively.The group error analyses of all inputs show that the GRU model has less than 5% AAPRE for all input ranges,which is superior to other models that have different AAPRE values of more than 10% at various ranges of inputs.
基金funded and supported by the Comprehensive Research Facility for Fusion Technology Program of China(No.2018-000052-73-01-001228)the HFIPS Director’s Fund(No.YZJJKX202301)+1 种基金Anhui Provincial Major Science and Technology Project(No.2023z020004)Task JB22001 from the Anhui Provincial Department of Economic and Information Technology。
文摘Electron density in fusion plasma is usually diagnosed using laser-aided interferometers. The phase difference signal obtained after phase demodulation is wrapped, which is also called a fringe jump. A method has been developed to unwrap the phase difference signal in real time using FPGA, specifically designed to handle fringe jumps in the hydrogen cyanide(HCN) laser interferometer on the EAST superconducting tokamak. This method is designed for a phase demodulator using the fast Fourier transform(FFT) method at the front end. The method is better adapted for hardware implementation compared to complex mathematical analysis algorithms, such as field programmable gate array(FPGA). It has been applied to process the phase measurement results of the HCN laser interferometer on EAST in real time. Electron density results show good confidence in the fringe jump unwrapping method. Further possible application in other laser interferometers, such as the POlarimeter-INTerferometer(POINT)system on EAST tokamak is also discussed.
基金supported by the JSPS KAKENHI(JP22K03386)supported by the JST SPRING(JPMJSP2132)。
文摘We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavior of a solution u near the boundary OD up to the third or higher term.
