A family of tests for the presence of regression effect under proportional and non-proportional hazards models is described. The non-proportional hazards model, although not completely general, is very broad and inclu...A family of tests for the presence of regression effect under proportional and non-proportional hazards models is described. The non-proportional hazards model, although not completely general, is very broad and includes a large number of possibilities. In the absence of restrictions, the regression coefficient, β(t), can be any real function of time. When β(t) = β, we recover the proportional hazards model which can then be taken as a special case of a non-proportional hazards model. We study tests of the null hypothesis;H0:β(t) = 0 for all t against alternatives such as;H1:∫β(t)dF(t) ≠ 0 or H1:β(t) ≠ 0 for some t. In contrast to now classical approaches based on partial likelihood and martingale theory, the development here is based on Brownian motion, Donsker’s theorem and theorems from O’Quigley [1] and Xu and O’Quigley [2]. The usual partial likelihood score test arises as a special case. Large sample theory follows without special arguments, such as the martingale central limit theorem, and is relatively straightforward.展开更多
Modeling and simulation have been carried out for Al-Pb alloys to investigate the Brownian coagulation effect on the microstructure development in a gas-atomized drop during the liquid-liquid decomposition. The result...Modeling and simulation have been carried out for Al-Pb alloys to investigate the Brownian coagulation effect on the microstructure development in a gas-atomized drop during the liquid-liquid decomposition. The results indicate that Brownian coagulation has a weak effect on the nucleation and a relatively strong effect on coarsening the minority phase droplets. The influence of Brownian coagulation on the liquid-liquid decomposition decreases with the increase in the diameter （or the decrease in the cooling rate） of the atomized drop.展开更多
Extensions of Merton’s model(EMM)considering the firm’s payments and generating new types of firm value distribution are suggested.In the open log-value/time space,these distributions evolve from initially normal to...Extensions of Merton’s model(EMM)considering the firm’s payments and generating new types of firm value distribution are suggested.In the open log-value/time space,these distributions evolve from initially normal to negatively skewed ones,and their means are concave-down functions of time.When payments are set to zero or proportional to the firm value,EMM turns into the Geometric Brownian model(GBM).We show that risk-neutral probabilities(RNPs)and the no-arbitraging principle(NAP)follow from GBM.When firm’s payments are considered,RNPs and NAP hold for the entire market for short times only,but for long-term investments,RNPs and NAP just temporarily hold for individual stocks as far as mean year returns of the firms issuing those stocks remain constant,and fail when the mean year returns decline.The developed method is applied to firm valuation to derive continuous-time equations for the firm present value and project NPV.展开更多
Stochasticity is introduced into a susceptible-exposed but not infectious-infectious-removed （SEIR） model describing epidemics＇ transmission, via the technique of parameter perturbation which is standard in stochas...Stochasticity is introduced into a susceptible-exposed but not infectious-infectious-removed （SEIR） model describing epidemics＇ transmission, via the technique of parameter perturbation which is standard in stochastic population modeling. The existence and uniqueness of the model have been proved in this paper. And E detailed analysis on global asymptotic stability is also carried out.展开更多
We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number Ro, a key parameter in epidemiology, is a threshold which determines the persistence or e...We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number Ro, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if Ro is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If Ro is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of Ro, when the stochastic system obeys some conditions and Ro is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.展开更多
This paper discusses the valuation of the Credit Default Swap based on a jump market, in which the asset price of a firm follows a double exponential jump diffusion process, the value of the debt is driven by a geomet...This paper discusses the valuation of the Credit Default Swap based on a jump market, in which the asset price of a firm follows a double exponential jump diffusion process, the value of the debt is driven by a geometric Brownian motion, and the default barrier follows a continuous stochastic process. Using the Gaver-Stehfest algorithm and the non-arbitrage asset pricing theory, we give the default probability of the first passage time, and more, derive the price of the Credit Default Swap.展开更多
In this work we introduce a Brownian motion in random environment which is a Brownian constructions by an exchangeable sequence based on Dirichlet processes samples. We next compute a stochastic calculus and an estima...In this work we introduce a Brownian motion in random environment which is a Brownian constructions by an exchangeable sequence based on Dirichlet processes samples. We next compute a stochastic calculus and an estimation of the parameters is computed in order to classify a functional data.展开更多
This paper considers the pricing problem of collateralized debt obligations tranches under a structural jump-diffusion model, where the asset value of each reference entity is generated by a geometric Brownian motion ...This paper considers the pricing problem of collateralized debt obligations tranches under a structural jump-diffusion model, where the asset value of each reference entity is generated by a geometric Brownian motion and jump with an asymmetric double exponential distribution. Conditioned on the common factor of individual entity, this paper gets the conditional distribution, and further obtains the loss distribution of the whole reference portfolio. Based on the semi-analytic approach, the fair spreads of collateralized debt obligations tranches, i.e., the prices of collateralized debt obligations tranches, are derived.展开更多
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
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
We have shown that classic works of Modigliani and Miller, Black and Scholes, Merton, Black and Cox, and Leland making the foundation of the modern asset pricing theory, are wrong due to misinterpretation of no arbitr...We have shown that classic works of Modigliani and Miller, Black and Scholes, Merton, Black and Cox, and Leland making the foundation of the modern asset pricing theory, are wrong due to misinterpretation of no arbitrage as the martingale no-arbitrage principle. This error explains appearance of the geometric Brownian model (GBM) for description of the firm value and other long-term assets considering the firm and its assets as self-financing portfolios with symmetric return distributions. It contradicts the empirical observations that returns on firms, stocks, and bonds are skewed. On the other side, the settings of the asset valuation problems, taking into account the default line and business securing expenses, BSEs, generate skewed return distributions for the firm and its securities. The Extended Merton model (EMM), taking into account BSEs and the default line, shows that the no-arbitrage principle should be understood as the non-martingale no arbitrage, when for sufficiently long periods both the predictable part of returns and the mean of the stochastic part of returns occur negative, and the value of the return deficit depends on time and the states of the firm and market. The EMM findings explain the problems with the S&P 500 VIX, the strange behavior of variance and skewness of stock returns before and after the crisis of 1987, etc.展开更多
文摘A family of tests for the presence of regression effect under proportional and non-proportional hazards models is described. The non-proportional hazards model, although not completely general, is very broad and includes a large number of possibilities. In the absence of restrictions, the regression coefficient, β(t), can be any real function of time. When β(t) = β, we recover the proportional hazards model which can then be taken as a special case of a non-proportional hazards model. We study tests of the null hypothesis;H0:β(t) = 0 for all t against alternatives such as;H1:∫β(t)dF(t) ≠ 0 or H1:β(t) ≠ 0 for some t. In contrast to now classical approaches based on partial likelihood and martingale theory, the development here is based on Brownian motion, Donsker’s theorem and theorems from O’Quigley [1] and Xu and O’Quigley [2]. The usual partial likelihood score test arises as a special case. Large sample theory follows without special arguments, such as the martingale central limit theorem, and is relatively straightforward.
基金The authors gratefully acknowledge the financial support from the National Natural Science Foundation （NNSF） of China and the International Cooperation Key Project of NNSF of China （Nos. 50395104, 50271076 and 50371092）the Natural Science Foundation of Liaoning Province （20050047）.
文摘Modeling and simulation have been carried out for Al-Pb alloys to investigate the Brownian coagulation effect on the microstructure development in a gas-atomized drop during the liquid-liquid decomposition. The results indicate that Brownian coagulation has a weak effect on the nucleation and a relatively strong effect on coarsening the minority phase droplets. The influence of Brownian coagulation on the liquid-liquid decomposition decreases with the increase in the diameter （or the decrease in the cooling rate） of the atomized drop.
基金The author is infinitely thankful to his friend and colleague M.Rubinstein for valuable discussions and an invariable interest to his work.The author is also thankful to C.Miller for his high estimation of the author’s efforts.Of course,all errors are author’s full responsibility.
文摘Extensions of Merton’s model(EMM)considering the firm’s payments and generating new types of firm value distribution are suggested.In the open log-value/time space,these distributions evolve from initially normal to negatively skewed ones,and their means are concave-down functions of time.When payments are set to zero or proportional to the firm value,EMM turns into the Geometric Brownian model(GBM).We show that risk-neutral probabilities(RNPs)and the no-arbitraging principle(NAP)follow from GBM.When firm’s payments are considered,RNPs and NAP hold for the entire market for short times only,but for long-term investments,RNPs and NAP just temporarily hold for individual stocks as far as mean year returns of the firms issuing those stocks remain constant,and fail when the mean year returns decline.The developed method is applied to firm valuation to derive continuous-time equations for the firm present value and project NPV.
基金the International Economics and Foreign Trade Subject Group Research Projects on the Special Development Fund(2013-2014) for Higher Education from the Central to Support the Local,China(No.Y13022)
文摘Stochasticity is introduced into a susceptible-exposed but not infectious-infectious-removed （SEIR） model describing epidemics＇ transmission, via the technique of parameter perturbation which is standard in stochastic population modeling. The existence and uniqueness of the model have been proved in this paper. And E detailed analysis on global asymptotic stability is also carried out.
基金supported by the National Natural Science Foundation of China(Grant No.11326078)the Project of Science and Technology of Heilongjiang Province of China(Grant No.12531187)
文摘We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number Ro, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if Ro is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If Ro is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of Ro, when the stochastic system obeys some conditions and Ro is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.
基金Supported by The National Natural Science Foundation of China(71261015)Humanity and Social Science Youth Foundation of Education Ministry in China(10YJC630334)Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region
文摘This paper discusses the valuation of the Credit Default Swap based on a jump market, in which the asset price of a firm follows a double exponential jump diffusion process, the value of the debt is driven by a geometric Brownian motion, and the default barrier follows a continuous stochastic process. Using the Gaver-Stehfest algorithm and the non-arbitrage asset pricing theory, we give the default probability of the first passage time, and more, derive the price of the Credit Default Swap.
文摘In this work we introduce a Brownian motion in random environment which is a Brownian constructions by an exchangeable sequence based on Dirichlet processes samples. We next compute a stochastic calculus and an estimation of the parameters is computed in order to classify a functional data.
基金Supported by the National Natural Science Foundation of China (70771018)the Natural Science Foundation of Shandong Province (2009ZRB019AV)Mathematical Subject Construction Funds and the Key Laboratory of Financial Information Engineering of Ludong University (2008)
文摘This paper considers the pricing problem of collateralized debt obligations tranches under a structural jump-diffusion model, where the asset value of each reference entity is generated by a geometric Brownian motion and jump with an asymmetric double exponential distribution. Conditioned on the common factor of individual entity, this paper gets the conditional distribution, and further obtains the loss distribution of the whole reference portfolio. Based on the semi-analytic approach, the fair spreads of collateralized debt obligations tranches, i.e., the prices of collateralized debt obligations tranches, are derived.
文摘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.
基金Supported by the Fundamental Research Funds of Lanzhou University of Finance and Economics(Lzufe2017C-09)
文摘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.
文摘We have shown that classic works of Modigliani and Miller, Black and Scholes, Merton, Black and Cox, and Leland making the foundation of the modern asset pricing theory, are wrong due to misinterpretation of no arbitrage as the martingale no-arbitrage principle. This error explains appearance of the geometric Brownian model (GBM) for description of the firm value and other long-term assets considering the firm and its assets as self-financing portfolios with symmetric return distributions. It contradicts the empirical observations that returns on firms, stocks, and bonds are skewed. On the other side, the settings of the asset valuation problems, taking into account the default line and business securing expenses, BSEs, generate skewed return distributions for the firm and its securities. The Extended Merton model (EMM), taking into account BSEs and the default line, shows that the no-arbitrage principle should be understood as the non-martingale no arbitrage, when for sufficiently long periods both the predictable part of returns and the mean of the stochastic part of returns occur negative, and the value of the return deficit depends on time and the states of the firm and market. The EMM findings explain the problems with the S&P 500 VIX, the strange behavior of variance and skewness of stock returns before and after the crisis of 1987, etc.
