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
Lithium-ion batteries(LIBs)are widely used in transportation,energy storage,and other fields.The prediction of the remaining useful life(RUL)of lithium batteries not only provides a reference for health management but...Lithium-ion batteries(LIBs)are widely used in transportation,energy storage,and other fields.The prediction of the remaining useful life(RUL)of lithium batteries not only provides a reference for health management but also serves as a basis for assessing the residual value of the battery.In order to improve the prediction accuracy of the RUL of LIBs,a two-phase RUL early prediction method combining neural network and Gaussian process regression(GPR)is proposed.In the initial phase,the features related to the capacity degradation of LIBs are utilized to train the neural network model,which is used to predict the initial cycle lifetime of 124 LIBs.The Pearson coefficient’s two most significant characteristic factors and the predicted normalized lifetime form a 3D space.The Euclidean distance between the test dataset and each cell in the training dataset and validation dataset is calculated,and the shortest distance is considered to have a similar degradation pattern,which is used to determine the initial Dual Exponential Model(DEM).In the second phase,GPR uses the DEM as the initial parameter to predict each test set’s early RUL(ERUL).By testing four batteries under different working conditions,the RMSE of all capacity estimation is less than 1.2%,and the accuracy percentage(AP)of remaining life prediction is more than 98%.Experiments show that the method does not need human intervention and has high prediction accuracy.展开更多
This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance （CEV） model. Assume that the insurer＇s surplus process follows a jump-diffusion process, the ...This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance （CEV） model. Assume that the insurer＇s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term＇s explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained.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 Major Science and Technology Projects for Independent Innovation of China FAW Group Co.,Ltd.(Grant Nos.20220301018GX and 20220301019GX).
文摘Lithium-ion batteries(LIBs)are widely used in transportation,energy storage,and other fields.The prediction of the remaining useful life(RUL)of lithium batteries not only provides a reference for health management but also serves as a basis for assessing the residual value of the battery.In order to improve the prediction accuracy of the RUL of LIBs,a two-phase RUL early prediction method combining neural network and Gaussian process regression(GPR)is proposed.In the initial phase,the features related to the capacity degradation of LIBs are utilized to train the neural network model,which is used to predict the initial cycle lifetime of 124 LIBs.The Pearson coefficient’s two most significant characteristic factors and the predicted normalized lifetime form a 3D space.The Euclidean distance between the test dataset and each cell in the training dataset and validation dataset is calculated,and the shortest distance is considered to have a similar degradation pattern,which is used to determine the initial Dual Exponential Model(DEM).In the second phase,GPR uses the DEM as the initial parameter to predict each test set’s early RUL(ERUL).By testing four batteries under different working conditions,the RMSE of all capacity estimation is less than 1.2%,and the accuracy percentage(AP)of remaining life prediction is more than 98%.Experiments show that the method does not need human intervention and has high prediction accuracy.
文摘This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance （CEV） model. Assume that the insurer＇s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term＇s explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained.
