Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure ri...Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.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
Quasi-elastic neutron scattering(QENS) has many applications that are directly related to the development of highperformance functional materials and biological macromolecules, especially those containing some water. ...Quasi-elastic neutron scattering(QENS) has many applications that are directly related to the development of highperformance functional materials and biological macromolecules, especially those containing some water. The analysis method of QENS spectra data is important to obtain parameters that can explain the structure of materials and the dynamics of water. In this paper, we present a revised jump-diffusion and rotation-diffusion model(rJRM) used for QENS spectra data analysis. By the rJRM, the QENS spectra from a pure magnesium-silicate-hydrate(MSH) sample are fitted well for the Q range from 0.3 ^(-1) to 1.9 ^(-1) and temperatures from 210 K up to 280 K. The fitted parameters can be divided into two kinds. The first kind describes the structure of the MSH sample, including the ratio of immobile water(or bound water) C and the confining radius of mobile water a_0. The second kind describes the dynamics of confined water in pores contained in the MSH sample, including the translational diffusion coefficient Dt, the average translational residence timeτ0, the rotational diffusion coefficient D_r, and the mean squared displacement(MSD) u^2. The r JRM is a new practical method suitable to fit QENS spectra from porous materials, where hydrogen atoms appear in both solid and liquid phases.展开更多
This paper deals with the dividend optimization problem for an insurance company, whose surplus follows a jump-diffusion process. The objective of the company is to maximize the expected total discounted dividends pai...This paper deals with the dividend optimization problem for an insurance company, whose surplus follows a jump-diffusion process. The objective of the company is to maximize the expected total discounted dividends paid out until the time of ruin. Under concavity assumption on the optimal value function, the paper states some general properties and, in particular, smoothness results on the optimal value function, whose analysis mainly relies on viscosity solutions of the associated Hamilton-Jacobi-Bellman （HJB） equations. Based on these properties, the explicit expression of the optimal value function is obtained. And some numerical calculations are presented as the application of the results.展开更多
In this paper,we study the asymptotic behaviors of implied volatility in an affine jump-diffusion model.By assuming that log stock prices under the risk-neutral measure follow an affine jump-diffusion model,we show th...In this paper,we study the asymptotic behaviors of implied volatility in an affine jump-diffusion model.By assuming that log stock prices under the risk-neutral measure follow an affine jump-diffusion model,we show that an explicit form of the moment-generating function for log stock price can be obtained by solving a set of ordinary differential equations.A large-time large deviation principle for log stock prices is derived by applying the Gartner-Ellis theorem.We characterize the asymptotic behaviors of implied volatility in the large-maturity and large-strike regimes using the rate function in the large deviation principle.The asymptotics of the implied volatility for fixed-maturity,large-strike and small-strike regimes are also studied.Numerical results are provided to validate thetheoretical work.展开更多
In this paper,we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou’s jumpdiffusion model which is governed by a system of partial integro-diffe...In this paper,we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou’s jumpdiffusion model which is governed by a system of partial integro-differential equations(PIDEs).We show that this scheme is consistent,stable and monotone as the mesh sizes in space and time approach zero,hence it ensures the convergence to the solution of continuous problem.Finally,numerical experiments are performed to demonstrate the efficiency,accuracy and robustness of the proposed method.展开更多
The present work applied the HydroGeoSphere (HGS) model in humid tropical area to Koué watershed scale to simulate flows in porous and fractured area of crystalline aquifers. It integrates rainfall, physiographic...The present work applied the HydroGeoSphere (HGS) model in humid tropical area to Koué watershed scale to simulate flows in porous and fractured area of crystalline aquifers. It integrates rainfall, physiographic, fractures, hydraulic drilling and hydrodynamic data. The simulation of flows in porous area concerned 5 test zones. The input database of the model is implemented on a triangular grid in porous area using Gridbuilder software and interactive block grid in fractured area. In order to use the model in these two environments, boundary condition was set. The infiltrations rate of the earth layers is estimated in the order to 10-5 ms-1. The model simulates the pumping with a good reproductivity of the drawdown profiles of groundwater at the drillings. The storage coefficients vary between 9.9 × 10-4 and 2 × 10-3. The hydraulic conductivities vary from 8.5 × 10-6 to 2 × 10-5. 73.9% of the drillings studied has a high hydraulic conductivity and shows a strong drawdown of the groundwater table. The study of the static levels of the ground water allowed indicating the distribution of the water resources in the drillings: 57% are deep in the first 10 meters, 36% between 10 and 20 m, and 7% in the higher level to 20 m deep in the earth.展开更多
This paper establishes a stochastic maximum principle for a stochastic control of mean-field model which is governed by a Lévy process involving continuous and impulse control.The authors also show the existence ...This paper establishes a stochastic maximum principle for a stochastic control of mean-field model which is governed by a Lévy process involving continuous and impulse control.The authors also show the existence and uniqueness of the solution to a jump-diffusion mean-field stochastic differential equation involving impulse control.As for its application,a mean-variance portfolio selection problem has been solved.展开更多
In this paper,we study the nonparametric estimation of the second infinitesimal moment by using the reweighted Nadaraya-Watson (RNW) approach of the underlying jump diffusion model.We establish strong consistency and ...In this paper,we study the nonparametric estimation of the second infinitesimal moment by using the reweighted Nadaraya-Watson (RNW) approach of the underlying jump diffusion model.We establish strong consistency and asymptotic normality for the estimate of the second infinitesimal moment of continuous time models using the reweighted Nadaraya-Watson estimator to the true function.展开更多
This paper considers the problem of numerically evaluating discrete barrier option prices when the underlying asset follows the jump-diffusion model with stochas-tic volatility and stochastic intensity.We derive the t...This paper considers the problem of numerically evaluating discrete barrier option prices when the underlying asset follows the jump-diffusion model with stochas-tic volatility and stochastic intensity.We derive the three-dimensional characteristic function of the log-asset price,the volatility and the jump intensity.We also provide the approximate formula of the discrete barrier option prices by the three-dimensional Fourier cosine series expansion(3D-COS)method.Numerical results show that the 3D-COS method is rather correct,fast and competent for pricing the discrete barrier options.展开更多
In this paper,we propose a new method to estimate the diffusion function in the jump-diffusion model.First,a threshold reweighted Nadaraya-Watson-type estimator is introduced.Then,we establish asymptotic normality for...In this paper,we propose a new method to estimate the diffusion function in the jump-diffusion model.First,a threshold reweighted Nadaraya-Watson-type estimator is introduced.Then,we establish asymptotic normality for the estimator and conduct Monte Carlo simulations through two examples to verify the better finite-sampling properties.Finally,our estimator is demonstrated through the actual data of the Shanghai Interbank Offered Rate in China.展开更多
In this paper,combining the threshold technique,we reconstruct Nadaraya-Watson estimation using Gamma asymmetric kernels for the unknown jump intensity function of a diffusion process with finite activity jumps.Under ...In this paper,combining the threshold technique,we reconstruct Nadaraya-Watson estimation using Gamma asymmetric kernels for the unknown jump intensity function of a diffusion process with finite activity jumps.Under mild conditions,we obtain the asymptotic normality for the proposed estimator.Moreover,we have verified the better finite-sampling properties such as bias correction and efficiency gains of the underlying estimator compared with other nonparametric estimators through a Monte Carlo experiment.展开更多
基金Supported by the NNSF of China(40675023)the PHD Foundation of Guangxi Normal University.
文摘Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.
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Quasi-elastic neutron scattering(QENS) has many applications that are directly related to the development of highperformance functional materials and biological macromolecules, especially those containing some water. The analysis method of QENS spectra data is important to obtain parameters that can explain the structure of materials and the dynamics of water. In this paper, we present a revised jump-diffusion and rotation-diffusion model(rJRM) used for QENS spectra data analysis. By the rJRM, the QENS spectra from a pure magnesium-silicate-hydrate(MSH) sample are fitted well for the Q range from 0.3 ^(-1) to 1.9 ^(-1) and temperatures from 210 K up to 280 K. The fitted parameters can be divided into two kinds. The first kind describes the structure of the MSH sample, including the ratio of immobile water(or bound water) C and the confining radius of mobile water a_0. The second kind describes the dynamics of confined water in pores contained in the MSH sample, including the translational diffusion coefficient Dt, the average translational residence timeτ0, the rotational diffusion coefficient D_r, and the mean squared displacement(MSD) u^2. The r JRM is a new practical method suitable to fit QENS spectra from porous materials, where hydrogen atoms appear in both solid and liquid phases.
文摘This paper deals with the dividend optimization problem for an insurance company, whose surplus follows a jump-diffusion process. The objective of the company is to maximize the expected total discounted dividends paid out until the time of ruin. Under concavity assumption on the optimal value function, the paper states some general properties and, in particular, smoothness results on the optimal value function, whose analysis mainly relies on viscosity solutions of the associated Hamilton-Jacobi-Bellman （HJB） equations. Based on these properties, the explicit expression of the optimal value function is obtained. And some numerical calculations are presented as the application of the results.
基金supported in part by the Natural Science Foundation of China(Grant No.12071361)the Natural Science Foundation of Guangdong Province(Grant No.2020A1515010822)Shenzhen Natural Science Fund(the Stable Support Plan Program 20220810152104001).
文摘In this paper,we study the asymptotic behaviors of implied volatility in an affine jump-diffusion model.By assuming that log stock prices under the risk-neutral measure follow an affine jump-diffusion model,we show that an explicit form of the moment-generating function for log stock price can be obtained by solving a set of ordinary differential equations.A large-time large deviation principle for log stock prices is derived by applying the Gartner-Ellis theorem.We characterize the asymptotic behaviors of implied volatility in the large-maturity and large-strike regimes using the rate function in the large deviation principle.The asymptotics of the implied volatility for fixed-maturity,large-strike and small-strike regimes are also studied.Numerical results are provided to validate thetheoretical work.
基金supported by the National Natural Science Foundation of China(Nos.11971354,and 11701221)the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities’Association(No.2019FH001-079)the Fundamental Research Funds for the Central Universities(No.22120210555).
文摘In this paper,we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou’s jumpdiffusion model which is governed by a system of partial integro-differential equations(PIDEs).We show that this scheme is consistent,stable and monotone as the mesh sizes in space and time approach zero,hence it ensures the convergence to the solution of continuous problem.Finally,numerical experiments are performed to demonstrate the efficiency,accuracy and robustness of the proposed method.
文摘The present work applied the HydroGeoSphere (HGS) model in humid tropical area to Koué watershed scale to simulate flows in porous and fractured area of crystalline aquifers. It integrates rainfall, physiographic, fractures, hydraulic drilling and hydrodynamic data. The simulation of flows in porous area concerned 5 test zones. The input database of the model is implemented on a triangular grid in porous area using Gridbuilder software and interactive block grid in fractured area. In order to use the model in these two environments, boundary condition was set. The infiltrations rate of the earth layers is estimated in the order to 10-5 ms-1. The model simulates the pumping with a good reproductivity of the drawdown profiles of groundwater at the drillings. The storage coefficients vary between 9.9 × 10-4 and 2 × 10-3. The hydraulic conductivities vary from 8.5 × 10-6 to 2 × 10-5. 73.9% of the drillings studied has a high hydraulic conductivity and shows a strong drawdown of the groundwater table. The study of the static levels of the ground water allowed indicating the distribution of the water resources in the drillings: 57% are deep in the first 10 meters, 36% between 10 and 20 m, and 7% in the higher level to 20 m deep in the earth.
基金supported by the National Science Foundation of China under Grant No.11671404the Fundamental Research Funds for the Central Universities of Central South University under Grant No.10553320171635.
文摘This paper establishes a stochastic maximum principle for a stochastic control of mean-field model which is governed by a Lévy process involving continuous and impulse control.The authors also show the existence and uniqueness of the solution to a jump-diffusion mean-field stochastic differential equation involving impulse control.As for its application,a mean-variance portfolio selection problem has been solved.
基金supported by National Natural Science Foundation of China (Grant Nos.10871177,11071213)Research Fund for the Doctor Program of Higher Education of China (Grant No.20090101110020)
文摘In this paper,we study the nonparametric estimation of the second infinitesimal moment by using the reweighted Nadaraya-Watson (RNW) approach of the underlying jump diffusion model.We establish strong consistency and asymptotic normality for the estimate of the second infinitesimal moment of continuous time models using the reweighted Nadaraya-Watson estimator to the true function.
文摘This paper considers the problem of numerically evaluating discrete barrier option prices when the underlying asset follows the jump-diffusion model with stochas-tic volatility and stochastic intensity.We derive the three-dimensional characteristic function of the log-asset price,the volatility and the jump intensity.We also provide the approximate formula of the discrete barrier option prices by the three-dimensional Fourier cosine series expansion(3D-COS)method.Numerical results show that the 3D-COS method is rather correct,fast and competent for pricing the discrete barrier options.
基金supported by the National Natural Science Foundation of China(Grant Nos.12071257 and 11971267)National Key R&D Program of China(Grant No.2018YFA0703900)+7 种基金Shandong Provincial Natural Science Foundation(Grant No.ZR2019ZD41)the Young Scholars Program of Shandong University.Yuping Song’s research is supported by the National Natural Science Foundation of China(Grant No.11901397)Ministry of Education,Humanities and Social Sciences project(Grant No.18YJCZH153)National Statistical Science Research Project(Grant No.2018LZ05)Youth Academic Backbone Cultivation Project of Shanghai Normal University(Grant No.310-AC7031-19-003021)General Research Fund of Shanghai Normal University(Grant No.SK201720)Key Subject of Quantitative Economics(Grant No.310-AC7031-19-004221)Academic Innovation Team of Shanghai Normal University(Grant No.310-AC7031-19-004228).
文摘In this paper,we propose a new method to estimate the diffusion function in the jump-diffusion model.First,a threshold reweighted Nadaraya-Watson-type estimator is introduced.Then,we establish asymptotic normality for the estimator and conduct Monte Carlo simulations through two examples to verify the better finite-sampling properties.Finally,our estimator is demonstrated through the actual data of the Shanghai Interbank Offered Rate in China.
基金supported by the National Natural Science Foundation of China(No.11701331)Shandong Provincial Natural Science Foundation(No.ZR2017QA007)+6 种基金Young Scholars Program of Shandong Universitysupported by Ministry of Education,Humanities and Social Sciences project(No.18YJCZH153)National Statistical Science Research Project(No.2018LZ05)Youth Academic Backbone Cultivation Project of Shanghai Normal University(No.310-AC7031-19-003021)General Research Fund of Shanghai Normal University(SK201720)Key Subject of Quantitative Economics(No.310-AC7031-19-004221)Academic Innovation Team(No.310-AC7031-19-004228)of Shanghai Normal University
文摘In this paper,combining the threshold technique,we reconstruct Nadaraya-Watson estimation using Gamma asymmetric kernels for the unknown jump intensity function of a diffusion process with finite activity jumps.Under mild conditions,we obtain the asymptotic normality for the proposed estimator.Moreover,we have verified the better finite-sampling properties such as bias correction and efficiency gains of the underlying estimator compared with other nonparametric estimators through a Monte Carlo experiment.
