In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating acco...In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.展开更多
Dynamical behaviors and stability properties of a flat space Friedmann-Robertson-Walker universe filled with pressureless dark matter and viscous dark energy are studied in the context of standard classical and loop q...Dynamical behaviors and stability properties of a flat space Friedmann-Robertson-Walker universe filled with pressureless dark matter and viscous dark energy are studied in the context of standard classical and loop quantum cosmology. Assuming that the dark energy has a constant bulk viscosity, it is found that the bulk viscosity effects influence only the quintessence model case leading to the existence of a viscous late time attractor solution of de- Sitter type, whereas the quantum geometry effects influence the phantom model case where the big rip singularity is removed. Moreover, our results of the Hubble parameter as a function of the redshift are in good agreement with the more recent data.展开更多
In this paper, the absolute ruin in the compound Poisson risk model with interest and a constant dividend barrier is investigated. First, integro-differential equations satisfied by the expected discounted dividend pa...In this paper, the absolute ruin in the compound Poisson risk model with interest and a constant dividend barrier is investigated. First, integro-differential equations satisfied by the expected discounted dividend payments are derived. The explicit expressions are obtained when the individual claim size is exponential distributed. Second, the moment generating function of the discounted dividends is considered, and integro-differential equations satisfied by the moment generating function of the discounted dividends are derived. Third, by a ＂differential＂ argument, the time to recovery to zero from a given negative surplus is considered. Finally, how long it takes for the surplus process to reach the dividend barrier is discussed.展开更多
Using our recently published electron’s charge electromagnetic flux manifold fiber model of the electron, described by analytical method and numerical simulations, we show how the fine structure constant is embedded ...Using our recently published electron’s charge electromagnetic flux manifold fiber model of the electron, described by analytical method and numerical simulations, we show how the fine structure constant is embedded as a geometrical proportionality constant in three dimensional space of its charge manifold and how this dictates the first QED term one-loop contribution of its anomalous magnetic moment making for the first time a connection of its intrinsic characteristics with physical geometrical dimensions and therefore demonstrating that the physical electron charge cannot be dimensionless. We show that the fine structure constant (FSC) α, and anomalous magnetic moment α<sub>μ</sub> of the electron is related to the sphericity of its charge distribution which is not perfectly spherical and thus has a shape, and therefore its self-confined charge possesses measurable physical dimensions. We also explain why these are not yet able to be measured by past and current experiments and how possible we could succeed.展开更多
A model for the internal structure of the electron using classical physics equations has been previously published by the author. The model employs both positive and negative charges and positive and negative masses. ...A model for the internal structure of the electron using classical physics equations has been previously published by the author. The model employs both positive and negative charges and positive and negative masses. The internal attributes of the electron structure were calculated for both ring and spherical shapes. Further examination of the model reveals an instability for the ring shape. The spherical shape appears to be stable, but relies on tensile or compressive forces of the electron material for stability. The model is modified in this document to eliminate the dependency on material forces. Uniform stability is provided solely by balancing electrical and centrifugal forces. This stability is achieved by slightly elongating the sphere along the spin axis to create a prolate ellipsoid. The semi-major axis of the ellipsoid is the spin axis of the electron, and is calculated to be 1.20% longer than the semi-minor axis, which is the radius of the equator. Although the shape deviates slightly from a perfect sphere, the electric dipole moment is zero. In the author’s previously published document, the attributes of the internal components of the electron, such as charge and mass, were calculated and expressed as ratios to the classically measured values for the composite electron. It is interesting to note that all of these ratios are nearly the same as the inverse of the Fine Structure Constant, with differences of less than 15%. The electron model assumed that the outer surface charge was fixed and uniform. By allowing the charge to be mobile and the shape to have a particular ellipticity, it is shown that the calculated charge and mass ratios for the model can be exactly equal to the Fine Structure Constant and the Constant plus one. The electron radius predicted by the model is 15% greater than the Classical Electron Radius.展开更多
In this paper we consider the problem of maximizing the total discounted utility of dividend payments for a Cramer-Lundberg risk model subject to both proportional and fixed transaction costs. We assume that dividend ...In this paper we consider the problem of maximizing the total discounted utility of dividend payments for a Cramer-Lundberg risk model subject to both proportional and fixed transaction costs. We assume that dividend payments are prohibited unless the surplus of insurance company has reached a level b. Given fixed level b, we derive a integro-differential equation satisfied by the value function. By solving this equation we obtain the analytical solutions of the value function and the optimal dividend strategy when claims are exponentially distributed. Finally we show how the threshold b can be determined so that the expected ruin time is not less than some T. Also, numerical examples are presented to illustrate our results.展开更多
基金supported by the National Natural Science Foundation of China(11101451)Ph.D.Programs Foundation of Ministry of Education of China(20110191110033)
文摘In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.
基金Supported by the Algerian Ministry of Education and ResearchDGRSDT
文摘Dynamical behaviors and stability properties of a flat space Friedmann-Robertson-Walker universe filled with pressureless dark matter and viscous dark energy are studied in the context of standard classical and loop quantum cosmology. Assuming that the dark energy has a constant bulk viscosity, it is found that the bulk viscosity effects influence only the quintessence model case leading to the existence of a viscous late time attractor solution of de- Sitter type, whereas the quantum geometry effects influence the phantom model case where the big rip singularity is removed. Moreover, our results of the Hubble parameter as a function of the redshift are in good agreement with the more recent data.
基金Supported by the National Natural Science Foundation of China (10971157)the Fundamental Research Funds for the Central Universities
文摘In this paper, the absolute ruin in the compound Poisson risk model with interest and a constant dividend barrier is investigated. First, integro-differential equations satisfied by the expected discounted dividend payments are derived. The explicit expressions are obtained when the individual claim size is exponential distributed. Second, the moment generating function of the discounted dividends is considered, and integro-differential equations satisfied by the moment generating function of the discounted dividends are derived. Third, by a ＂differential＂ argument, the time to recovery to zero from a given negative surplus is considered. Finally, how long it takes for the surplus process to reach the dividend barrier is discussed.
文摘Using our recently published electron’s charge electromagnetic flux manifold fiber model of the electron, described by analytical method and numerical simulations, we show how the fine structure constant is embedded as a geometrical proportionality constant in three dimensional space of its charge manifold and how this dictates the first QED term one-loop contribution of its anomalous magnetic moment making for the first time a connection of its intrinsic characteristics with physical geometrical dimensions and therefore demonstrating that the physical electron charge cannot be dimensionless. We show that the fine structure constant (FSC) α, and anomalous magnetic moment α<sub>μ</sub> of the electron is related to the sphericity of its charge distribution which is not perfectly spherical and thus has a shape, and therefore its self-confined charge possesses measurable physical dimensions. We also explain why these are not yet able to be measured by past and current experiments and how possible we could succeed.
文摘A model for the internal structure of the electron using classical physics equations has been previously published by the author. The model employs both positive and negative charges and positive and negative masses. The internal attributes of the electron structure were calculated for both ring and spherical shapes. Further examination of the model reveals an instability for the ring shape. The spherical shape appears to be stable, but relies on tensile or compressive forces of the electron material for stability. The model is modified in this document to eliminate the dependency on material forces. Uniform stability is provided solely by balancing electrical and centrifugal forces. This stability is achieved by slightly elongating the sphere along the spin axis to create a prolate ellipsoid. The semi-major axis of the ellipsoid is the spin axis of the electron, and is calculated to be 1.20% longer than the semi-minor axis, which is the radius of the equator. Although the shape deviates slightly from a perfect sphere, the electric dipole moment is zero. In the author’s previously published document, the attributes of the internal components of the electron, such as charge and mass, were calculated and expressed as ratios to the classically measured values for the composite electron. It is interesting to note that all of these ratios are nearly the same as the inverse of the Fine Structure Constant, with differences of less than 15%. The electron model assumed that the outer surface charge was fixed and uniform. By allowing the charge to be mobile and the shape to have a particular ellipticity, it is shown that the calculated charge and mass ratios for the model can be exactly equal to the Fine Structure Constant and the Constant plus one. The electron radius predicted by the model is 15% greater than the Classical Electron Radius.
基金Supported by the National Natural Science Foundation of China(Nos.71231008,71201173,71301031)Natural Science Foundation of Guangdong Province of China(No.S2012040006838)+1 种基金the High-level Talent Project of Guangdong "Research on Models and Strategies for Optimal Reinsurance,Investment and Dividend"the Post-Doctoral Foundation of China(No.2012M510195)
文摘In this paper we consider the problem of maximizing the total discounted utility of dividend payments for a Cramer-Lundberg risk model subject to both proportional and fixed transaction costs. We assume that dividend payments are prohibited unless the surplus of insurance company has reached a level b. Given fixed level b, we derive a integro-differential equation satisfied by the value function. By solving this equation we obtain the analytical solutions of the value function and the optimal dividend strategy when claims are exponentially distributed. Finally we show how the threshold b can be determined so that the expected ruin time is not less than some T. Also, numerical examples are presented to illustrate our results.
