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
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
The correlation between the Schrödinger equation and the diffusion equation revealed that the relation of material wave is not a hypothesis but an actual one valid in a material regardless of the photon energ...The correlation between the Schrödinger equation and the diffusion equation revealed that the relation of material wave is not a hypothesis but an actual one valid in a material regardless of the photon energy. Using the relations of material wave and uncertain principle, the quantum effect on elementary process of diffusion is discussed. As a result, the diffusivity is obtained as a universal expression applicable to any problem of diffusion phenomena. The Gauss theorem in theory and the Kirkendall effect in experimentation reveal the necessity of the coordinate transformation for a diffusion equation. The mathematical method for solving an interdiffusion problem of many elements system is established. The phase shift of the obtained analytical solution indicates the correlation between the solutions of each diffusion equation expressed by a fixed coordinate system and by a moving coordinate system. Based on the coordinate transformation theory, some unsolved problems of diffusion theory are reasonably solved and also some new important findings are discussed in relation to matters in the existing diffusion theory.展开更多
The Brownian motion of spherical and ellipsoidal self-propelled particles was simulated without considering the effect of inertia and using the Langevin equation and the diffusion coefficient of ellipsoidal particles ...The Brownian motion of spherical and ellipsoidal self-propelled particles was simulated without considering the effect of inertia and using the Langevin equation and the diffusion coefficient of ellipsoidal particles derived by Perrin.The P´eclet number(Pe)was introduced to measure the relative strengths of self-propelled and Brownian motions.We found that the motion state of spherical and ellipsoid self-propelled particles changed significantly under the influence of Brownian motion.For spherical particles,there were three primary states of motion:1)when Pe<30,the particles were still significantly affected by Brownian motion;2)when Pe>30,the self-propelled velocities of the particles were increasing;and 3)when Pe>100,the particles were completely controlled by the self-propelled velocities and the Brownian motion was suppressed.In the simulation of the ellipsoidal self-propelled particles,we found that the larger the aspect ratio of the particles,the more susceptible they were to the influence of Brownian motion.In addition,the value interval of Pe depended on the aspect ratio.Finally,we found that the directional motion ability of the ellipsoidal self-propelled particles was much weaker than that of the spherical self-propelled particles.展开更多
Brown运动是一个具有连续时间参数和连续状态空间的随机过程,有两种不同定义下的局部时,一种是P.Levy提出的"mesure du voisinage"的概念,也即Brown运动{Wt,Ft}t≥0的局部时Lt(x)=limε→014εmeas{0≤s≤t;|Ws-x|≤ε},t∈[0...Brown运动是一个具有连续时间参数和连续状态空间的随机过程,有两种不同定义下的局部时,一种是P.Levy提出的"mesure du voisinage"的概念,也即Brown运动{Wt,Ft}t≥0的局部时Lt(x)=limε→014εmeas{0≤s≤t;|Ws-x|≤ε},t∈[0,∞),.x∈R.另一种是由游程理论定义的局部时lt(x),并给出这两种局部时之间的关系Lt(0)=24lt(0).展开更多
文摘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.
文摘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.
文摘The correlation between the Schrödinger equation and the diffusion equation revealed that the relation of material wave is not a hypothesis but an actual one valid in a material regardless of the photon energy. Using the relations of material wave and uncertain principle, the quantum effect on elementary process of diffusion is discussed. As a result, the diffusivity is obtained as a universal expression applicable to any problem of diffusion phenomena. The Gauss theorem in theory and the Kirkendall effect in experimentation reveal the necessity of the coordinate transformation for a diffusion equation. The mathematical method for solving an interdiffusion problem of many elements system is established. The phase shift of the obtained analytical solution indicates the correlation between the solutions of each diffusion equation expressed by a fixed coordinate system and by a moving coordinate system. Based on the coordinate transformation theory, some unsolved problems of diffusion theory are reasonably solved and also some new important findings are discussed in relation to matters in the existing diffusion theory.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12372251 and 12132015)the Fundamental Research Funds for the Provincial Universities of Zhejiang(Grant No.2023YW69).
文摘The Brownian motion of spherical and ellipsoidal self-propelled particles was simulated without considering the effect of inertia and using the Langevin equation and the diffusion coefficient of ellipsoidal particles derived by Perrin.The P´eclet number(Pe)was introduced to measure the relative strengths of self-propelled and Brownian motions.We found that the motion state of spherical and ellipsoid self-propelled particles changed significantly under the influence of Brownian motion.For spherical particles,there were three primary states of motion:1)when Pe<30,the particles were still significantly affected by Brownian motion;2)when Pe>30,the self-propelled velocities of the particles were increasing;and 3)when Pe>100,the particles were completely controlled by the self-propelled velocities and the Brownian motion was suppressed.In the simulation of the ellipsoidal self-propelled particles,we found that the larger the aspect ratio of the particles,the more susceptible they were to the influence of Brownian motion.In addition,the value interval of Pe depended on the aspect ratio.Finally,we found that the directional motion ability of the ellipsoidal self-propelled particles was much weaker than that of the spherical self-propelled particles.
文摘Brown运动是一个具有连续时间参数和连续状态空间的随机过程,有两种不同定义下的局部时,一种是P.Levy提出的"mesure du voisinage"的概念,也即Brown运动{Wt,Ft}t≥0的局部时Lt(x)=limε→014εmeas{0≤s≤t;|Ws-x|≤ε},t∈[0,∞),.x∈R.另一种是由游程理论定义的局部时lt(x),并给出这两种局部时之间的关系Lt(0)=24lt(0).
