A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stocha...A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options.展开更多
The objective of this paper is to develop a variable learning rate for neural modeling of multivariable nonlinear stochastic system. The corresponding parameter is obtained by gradient descent method optimization. The...The objective of this paper is to develop a variable learning rate for neural modeling of multivariable nonlinear stochastic system. The corresponding parameter is obtained by gradient descent method optimization. The effectiveness of the suggested algorithm applied to the identification of behavior of two nonlinear stochastic systems is demonstrated by simulation experiments.展开更多
This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. ...This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. The nonlinear incidence rate describes the psychological impact of certain serious rumors on social groups when the number of individuals spreading rumors becomes larger. The main contributions of this work are the development of a new rumor propagation model and some results of deterministic and stochastic analysis of the rumor propagation model. The results show the influence of nonlinear propagation rate and stochastic fluctuation on the dynamic behavior of the rumor propagation model by using Lyapunov function method and stochastic related knowledge. Numerical examples and simulation results are given to illustrate the results obtained.展开更多
Asian options are the popular second generation derivative products and embedded in many structured notes to enhance upside performance.The embedded options,as a result,usually have a long duration.The movement of int...Asian options are the popular second generation derivative products and embedded in many structured notes to enhance upside performance.The embedded options,as a result,usually have a long duration.The movement of interest rates becomes more important in pricing such long-dated options.In this paper,the pricing of Asian options under stochastic interest rates is studied.Assuming Hull and White model for the interest rates,a closed-form formula for geometric-average options is derived.As a by-product,pricing formula is also given for plan-vanilla options under stochastic interest rates.展开更多
In this paper, the methods developed by?[1] are used to analyze flowback data, which involves modeling flow both before and after the breakthrough of formation fluids. Despite the versatility of these techniques, achi...In this paper, the methods developed by?[1] are used to analyze flowback data, which involves modeling flow both before and after the breakthrough of formation fluids. Despite the versatility of these techniques, achieving an optimal combination of parameters is often difficult with a single deterministic analysis. Because of the uncertainty in key model parameters, this problem is an ideal candidate for uncertainty quantification and advanced assisted history-matching techniques, including Monte Carlo (MC) simulation and genetic algorithms (GAs) amongst others. MC simulation, for example, can be used for both the purpose of assisted history-matching and uncertainty quantification of key fracture parameters. In this work, several techniques are tested including both single-objective (SO) and multi-objective (MO) algorithms for history-matching and uncertainty quantification, using a light tight oil (LTO) field case. The results of this analysis suggest that many different algorithms can be used to achieve similar optimization results, making these viable methods for developing an optimal set of key uncertain fracture parameters. An indication of uncertainty can also be achieved, which assists in understanding the range of parameters which can be used to successfully match the flowback data.展开更多
This paper focuses on how to measure the interest rate risk. The conventional measure methods of interest rate risk are reviewed and the duration concept is generalized to stochastic duration in the Markovian HJM fram...This paper focuses on how to measure the interest rate risk. The conventional measure methods of interest rate risk are reviewed and the duration concept is generalized to stochastic duration in the Markovian HJM framework. The generalized stochastic duration of the coupon bond is defined as the time to maturity of a zero coupon bond having the same instantaneous variance as the coupon bond. According to this definition., the authors first present the framework of Markovian HJM model, then deduce the measures of stochastic duration in some special cases which cover some extant interest term structure.展开更多
The purpose of this paper is to present the theorical connection between the Itôstochastic calculus and the Financial Econometrics. This paper has two contributions. First, we give the backgrounds on how the ...The purpose of this paper is to present the theorical connection between the Itôstochastic calculus and the Financial Econometrics. This paper has two contributions. First, we give the backgrounds on how the stochastic calculus is used to model the real data with the uncertainties. Finally, by using Consumer Price Index (CPI) from the Central Bank of Congo and combining the Itôstochastic calculus and the AR (1)-GARCH (1, 1) model, we estimate the stochastic volatility of inflation rate measuring efficency of monetary policy. Thus the stochastic integrals are the powerful tools of mathematical modelling and econometric analysis.展开更多
Markov modeling of HIV/AIDS progression was done under the assumption that the state holding time (waiting time) had a constant hazard. This paper discusses the properties of the hazard function of the Exponential dis...Markov modeling of HIV/AIDS progression was done under the assumption that the state holding time (waiting time) had a constant hazard. This paper discusses the properties of the hazard function of the Exponential distributions and its modifications namely;Parameter proportion hazard (PH) and Accelerated failure time models (AFT) and their effectiveness in modeling the state holding time in Markov modeling of HIV/AIDS progression with and without risk factors. Patients were categorized by gender and age with female gender being the baseline. Data simulated using R software was fitted to each model, and the model parameters were estimated. The estimated P and Z values were then used to test the null hypothesis that the state waiting time data followed an Exponential distribution. Model identification criteria;Akaike information criteria (AIC), Bayesian information criteria (BIC), log-likelihood (LL), and R2 were used to evaluate the performance of the models. For the Survival Regression model, P and Z values supported the non-rejection of the null hypothesis for mixed gender without interaction and supported the rejection of the same for mixed gender with interaction term and males aged 50 - 60 years. Both Parameters supported the non-rejection of the null hypothesis in the rest of the age groups. For Gender male with interaction both P and Z values supported rejection in all the age groups except the age group 20 - 30 years. For Cox Proportional hazard and AFT models, both P and Z values supported the non-rejection of the null hypothesis across all age groups. The P-values for the three models supported different decisions for and against the Null hypothesis with AFT and Cox values supporting similar decisions in most of the age groups. Among the models considered, the regression assumption provided a superior fit based on (AIC), (BIC), (LL), and R2 Model identification criteria. This was particularly evident in age and gender subgroups where the data exhibited non-proportional hazards and violated the assumptions required for the Cox Proportional Hazard model. Moreover, the simplicity of the regression model, along with its ability to capture essential state transitions without over fitting, made it a more appropriate choice.展开更多
This work proposes a unified damage model for concrete within the framework of stochastic damage mechanics. Based on the micro-meso stochastic fracture model(MMSF), the nonlinear energy dissipation process of the micr...This work proposes a unified damage model for concrete within the framework of stochastic damage mechanics. Based on the micro-meso stochastic fracture model(MMSF), the nonlinear energy dissipation process of the microspring from nanoscale to microscale is investigated. In nanoscale, the rate process theory is adopted to describe the crack growth rate;therefore, the corresponding energy dissipation caused by a representative crack propagation can be obtained. The scale gap from nanoscale to microscale is bridged by a crack hierarchy model. Thus, the total energy dissipated by all cracks from the nanoscale to the microscale is gained. It is found that the fracture strain of the microspring can be derived from the above multi-scale energy dissipation analysis. When energy dissipation is regarded as some microdamage to the microspring, the constitutive law of the microspring is no longer linearly elastic, as previously assumed. By changing the expression of the damage evolution law from fracture strain to energy dissipation threshold, the new damage evolution model is derived. The proposed model can not only replicate the original static model but also extend to cases of rate dependence. By deriving the fracture strain under different strain rates, the rate sensitivity of concrete materials can be reflected. The model parameters can be conveniently obtained by identifying them with experimental data. Finally, several numerical examples are presented to verify the proposed model.展开更多
In this paper,a stochastic SIQS epidemic model perturbed by both white and telephone noises is investigated.By constructing several suitable Lyapunov functions,we obtain sufficient conditions for the existence of ergo...In this paper,a stochastic SIQS epidemic model perturbed by both white and telephone noises is investigated.By constructing several suitable Lyapunov functions,we obtain sufficient conditions for the existence of ergodic stationary distribution of the positive solution.Moreover,by solving the Fokker-Planck equation,we obtain the exact expression of probability density function around the quasi-equilibrium of the stochastic model.In addition,sufficient conditions for the extinction are established.Finally,the results of this paper are further verified by numerical simulation.展开更多
This paper proposes an efficient option pricing model that incorporates stochastic interest rate(SIR),stochastic volatility(SV),and double exponential jump into the jump-diffusion settings.The model comprehensively co...This paper proposes an efficient option pricing model that incorporates stochastic interest rate(SIR),stochastic volatility(SV),and double exponential jump into the jump-diffusion settings.The model comprehensively considers the leptokurtosis and heteroscedasticity of the underlying asset’s returns,rare events,and an SIR.Using the model,we deduce the pricing characteristic function and pricing formula of a European option.Then,we develop the Markov chain Monte Carlo method with latent variable to solve the problem of parameter estimation under the double exponential jump-diffusion model with SIR and SV.For verification purposes,we conduct time efficiency analysis,goodness of fit analysis,and jump/drift term analysis of the proposed model.In addition,we compare the pricing accuracy of the proposed model with those of the Black-Scholes and the Kou(2002)models.The empirical results show that the proposed option pricing model has high time efficiency,and the goodness of fit and pricing accuracy are significantly higher than those of the other two models.展开更多
Based on the work in Ding and Ding(2008),we develop a modifed stochastic gradient(SG)parameter estimation algorithm for a dual-rate Box-Jenkins model by using an auxiliary model.We simplify the complex dual-rate Box-J...Based on the work in Ding and Ding(2008),we develop a modifed stochastic gradient(SG)parameter estimation algorithm for a dual-rate Box-Jenkins model by using an auxiliary model.We simplify the complex dual-rate Box-Jenkins model to two fnite impulse response(FIR)models,present an auxiliary model to estimate the missing outputs and the unknown noise variables,and compute all the unknown parameters of the system with colored noises.Simulation results indicate that the proposed method is efective.展开更多
In the stock market, some popular technical analysis indicators （e.g. Bollinger Bands, RSI, ROC, ...） are widely used by traders. They use the daily （hourly, weekly, ...） stock prices as samples of certain statist...In the stock market, some popular technical analysis indicators （e.g. Bollinger Bands, RSI, ROC, ...） are widely used by traders. They use the daily （hourly, weekly, ...） stock prices as samples of certain statistics and use the observed relative frequency to show the validity of those well-known indicators. However, those samples are not independent, so the classical sample survey theory does not apply. In earlier research, we discussed the law of large numbers related to those observations when one assumes Black-Scholes＇ stock price model. In this paper, we extend the above results to the more popular stochastic volatility model.展开更多
In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by...In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by a Cox-Ingersoll-Ross （CIR） model. For the stock price process, we consider both the case of constant volatility （driven by an O U process） and the case of stochastic volatility （driven by a CIR model）. In each case, under certain conditions, we obtain the minimal upper bound for ruin probability as well as the corresponding optimal investment strategy by a pure probabilistic method.展开更多
基金National Natural Science Foundations of China(Nos.11471175,11171221)
文摘A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options.
文摘The objective of this paper is to develop a variable learning rate for neural modeling of multivariable nonlinear stochastic system. The corresponding parameter is obtained by gradient descent method optimization. The effectiveness of the suggested algorithm applied to the identification of behavior of two nonlinear stochastic systems is demonstrated by simulation experiments.
文摘This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. The nonlinear incidence rate describes the psychological impact of certain serious rumors on social groups when the number of individuals spreading rumors becomes larger. The main contributions of this work are the development of a new rumor propagation model and some results of deterministic and stochastic analysis of the rumor propagation model. The results show the influence of nonlinear propagation rate and stochastic fluctuation on the dynamic behavior of the rumor propagation model by using Lyapunov function method and stochastic related knowledge. Numerical examples and simulation results are given to illustrate the results obtained.
文摘Asian options are the popular second generation derivative products and embedded in many structured notes to enhance upside performance.The embedded options,as a result,usually have a long duration.The movement of interest rates becomes more important in pricing such long-dated options.In this paper,the pricing of Asian options under stochastic interest rates is studied.Assuming Hull and White model for the interest rates,a closed-form formula for geometric-average options is derived.As a by-product,pricing formula is also given for plan-vanilla options under stochastic interest rates.
文摘In this paper, the methods developed by?[1] are used to analyze flowback data, which involves modeling flow both before and after the breakthrough of formation fluids. Despite the versatility of these techniques, achieving an optimal combination of parameters is often difficult with a single deterministic analysis. Because of the uncertainty in key model parameters, this problem is an ideal candidate for uncertainty quantification and advanced assisted history-matching techniques, including Monte Carlo (MC) simulation and genetic algorithms (GAs) amongst others. MC simulation, for example, can be used for both the purpose of assisted history-matching and uncertainty quantification of key fracture parameters. In this work, several techniques are tested including both single-objective (SO) and multi-objective (MO) algorithms for history-matching and uncertainty quantification, using a light tight oil (LTO) field case. The results of this analysis suggest that many different algorithms can be used to achieve similar optimization results, making these viable methods for developing an optimal set of key uncertain fracture parameters. An indication of uncertainty can also be achieved, which assists in understanding the range of parameters which can be used to successfully match the flowback data.
文摘This paper focuses on how to measure the interest rate risk. The conventional measure methods of interest rate risk are reviewed and the duration concept is generalized to stochastic duration in the Markovian HJM framework. The generalized stochastic duration of the coupon bond is defined as the time to maturity of a zero coupon bond having the same instantaneous variance as the coupon bond. According to this definition., the authors first present the framework of Markovian HJM model, then deduce the measures of stochastic duration in some special cases which cover some extant interest term structure.
文摘The purpose of this paper is to present the theorical connection between the Itôstochastic calculus and the Financial Econometrics. This paper has two contributions. First, we give the backgrounds on how the stochastic calculus is used to model the real data with the uncertainties. Finally, by using Consumer Price Index (CPI) from the Central Bank of Congo and combining the Itôstochastic calculus and the AR (1)-GARCH (1, 1) model, we estimate the stochastic volatility of inflation rate measuring efficency of monetary policy. Thus the stochastic integrals are the powerful tools of mathematical modelling and econometric analysis.
文摘Markov modeling of HIV/AIDS progression was done under the assumption that the state holding time (waiting time) had a constant hazard. This paper discusses the properties of the hazard function of the Exponential distributions and its modifications namely;Parameter proportion hazard (PH) and Accelerated failure time models (AFT) and their effectiveness in modeling the state holding time in Markov modeling of HIV/AIDS progression with and without risk factors. Patients were categorized by gender and age with female gender being the baseline. Data simulated using R software was fitted to each model, and the model parameters were estimated. The estimated P and Z values were then used to test the null hypothesis that the state waiting time data followed an Exponential distribution. Model identification criteria;Akaike information criteria (AIC), Bayesian information criteria (BIC), log-likelihood (LL), and R2 were used to evaluate the performance of the models. For the Survival Regression model, P and Z values supported the non-rejection of the null hypothesis for mixed gender without interaction and supported the rejection of the same for mixed gender with interaction term and males aged 50 - 60 years. Both Parameters supported the non-rejection of the null hypothesis in the rest of the age groups. For Gender male with interaction both P and Z values supported rejection in all the age groups except the age group 20 - 30 years. For Cox Proportional hazard and AFT models, both P and Z values supported the non-rejection of the null hypothesis across all age groups. The P-values for the three models supported different decisions for and against the Null hypothesis with AFT and Cox values supporting similar decisions in most of the age groups. Among the models considered, the regression assumption provided a superior fit based on (AIC), (BIC), (LL), and R2 Model identification criteria. This was particularly evident in age and gender subgroups where the data exhibited non-proportional hazards and violated the assumptions required for the Cox Proportional Hazard model. Moreover, the simplicity of the regression model, along with its ability to capture essential state transitions without over fitting, made it a more appropriate choice.
基金supported by the National Natural Science Foundation of China(Grant No. 51538010)。
文摘This work proposes a unified damage model for concrete within the framework of stochastic damage mechanics. Based on the micro-meso stochastic fracture model(MMSF), the nonlinear energy dissipation process of the microspring from nanoscale to microscale is investigated. In nanoscale, the rate process theory is adopted to describe the crack growth rate;therefore, the corresponding energy dissipation caused by a representative crack propagation can be obtained. The scale gap from nanoscale to microscale is bridged by a crack hierarchy model. Thus, the total energy dissipated by all cracks from the nanoscale to the microscale is gained. It is found that the fracture strain of the microspring can be derived from the above multi-scale energy dissipation analysis. When energy dissipation is regarded as some microdamage to the microspring, the constitutive law of the microspring is no longer linearly elastic, as previously assumed. By changing the expression of the damage evolution law from fracture strain to energy dissipation threshold, the new damage evolution model is derived. The proposed model can not only replicate the original static model but also extend to cases of rate dependence. By deriving the fracture strain under different strain rates, the rate sensitivity of concrete materials can be reflected. The model parameters can be conveniently obtained by identifying them with experimental data. Finally, several numerical examples are presented to verify the proposed model.
基金supported by the Natural Science Foundation of Changchun Normal University(No.2021-005).
文摘In this paper,a stochastic SIQS epidemic model perturbed by both white and telephone noises is investigated.By constructing several suitable Lyapunov functions,we obtain sufficient conditions for the existence of ergodic stationary distribution of the positive solution.Moreover,by solving the Fokker-Planck equation,we obtain the exact expression of probability density function around the quasi-equilibrium of the stochastic model.In addition,sufficient conditions for the extinction are established.Finally,the results of this paper are further verified by numerical simulation.
基金supported by the grants from the National Natural Science Foundation of China(NSFC No.71471161)the Key Programs of the National Natural Science Foundation of China(NSFC Nos.71631005 and 71433001)+1 种基金the National Natural Science Foundation of China(NSFC No.71703142)Zhejiang College StudentsʹScience Innovation Project(Xin Miao Project)on“Research on Integrated Risk Measurement of Structured Financial Products Based on Affine Jump Diffusion Process”(No.2016R414069).
文摘This paper proposes an efficient option pricing model that incorporates stochastic interest rate(SIR),stochastic volatility(SV),and double exponential jump into the jump-diffusion settings.The model comprehensively considers the leptokurtosis and heteroscedasticity of the underlying asset’s returns,rare events,and an SIR.Using the model,we deduce the pricing characteristic function and pricing formula of a European option.Then,we develop the Markov chain Monte Carlo method with latent variable to solve the problem of parameter estimation under the double exponential jump-diffusion model with SIR and SV.For verification purposes,we conduct time efficiency analysis,goodness of fit analysis,and jump/drift term analysis of the proposed model.In addition,we compare the pricing accuracy of the proposed model with those of the Black-Scholes and the Kou(2002)models.The empirical results show that the proposed option pricing model has high time efficiency,and the goodness of fit and pricing accuracy are significantly higher than those of the other two models.
基金Project supported by the National Natural Science Foundation of China(No.60973043)the Natural Science Foundation of Jiangsu Province,China(No.BK20131109)
文摘Based on the work in Ding and Ding(2008),we develop a modifed stochastic gradient(SG)parameter estimation algorithm for a dual-rate Box-Jenkins model by using an auxiliary model.We simplify the complex dual-rate Box-Jenkins model to two fnite impulse response(FIR)models,present an auxiliary model to estimate the missing outputs and the unknown noise variables,and compute all the unknown parameters of the system with colored noises.Simulation results indicate that the proposed method is efective.
基金Partially supported by National Natural Science Foundation of China （Grant No. 10971068）, National Basic Research Program of China （973 Program） （Grant No. 2007CB814904） and Key Subject Construction Project of Shanghai Education Commission （Grant No. J51601）
文摘In the stock market, some popular technical analysis indicators （e.g. Bollinger Bands, RSI, ROC, ...） are widely used by traders. They use the daily （hourly, weekly, ...） stock prices as samples of certain statistics and use the observed relative frequency to show the validity of those well-known indicators. However, those samples are not independent, so the classical sample survey theory does not apply. In earlier research, we discussed the law of large numbers related to those observations when one assumes Black-Scholes＇ stock price model. In this paper, we extend the above results to the more popular stochastic volatility model.
基金Supported by National Basic Research Program of China (973 Program, Grant No. 2007CB814905)National Natural Science Foundation of China (Grant No. 10871102)
文摘In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by a Cox-Ingersoll-Ross （CIR） model. For the stock price process, we consider both the case of constant volatility （driven by an O U process） and the case of stochastic volatility （driven by a CIR model）. In each case, under certain conditions, we obtain the minimal upper bound for ruin probability as well as the corresponding optimal investment strategy by a pure probabilistic method.
