The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average d...The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.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
The H_∞state estimation problem for a class of stochastic neural networks with Markovian jumping parameters and leakage delay is investigated in this paper.By employing a suitable Lyapunov functional and inequality t...The H_∞state estimation problem for a class of stochastic neural networks with Markovian jumping parameters and leakage delay is investigated in this paper.By employing a suitable Lyapunov functional and inequality technic,the suffcient conditions for exponential stability as well as prescribed H_∞norm level of the state estimation error system are proposed and verified,and all obtained results are expressed in terms of strict linear matrix inequalities(LMIs).Examples and simulations are presented to show the effectiveness of the proposed methods,at the same time,the effect of leakage delay on stability of neural networks system and on the attenuation level of state estimator are discussed.展开更多
This paper researches the strict dissipative control problem for uncertain fuzzy neutral Markov jump systems by Takagi-Sugeno fuzzy rules.The asynchronous phenomenon is considered between the uncertain fuzzy neutral M...This paper researches the strict dissipative control problem for uncertain fuzzy neutral Markov jump systems by Takagi-Sugeno fuzzy rules.The asynchronous phenomenon is considered between the uncertain fuzzy neutral Markov jump systems modes and asynchronous fuzzy P-D feedback controller modes,which is described by a hidden Markov model.Via using linear matrix inequalities,the desired asynchronous fuzzy P-D feedback controller is obtained,which can ensure that the closed-loop uncertain fuzzy neutral Markov jump systems satisfies robustly exponential mean square stabilization with strict dissipativity.A numerical example and a single-link robot arm are utilized to demonstrate the effectiveness of the method.展开更多
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 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the National Natural Science Foundation of China (60674027, 60574007)Doctoral Foundation of Education Ministry of China (20050446001).
文摘The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.
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supported by the Research Fund for the Doctoral Program of Guang Dong Province of China (No. 2015A030310336)
文摘The H_∞state estimation problem for a class of stochastic neural networks with Markovian jumping parameters and leakage delay is investigated in this paper.By employing a suitable Lyapunov functional and inequality technic,the suffcient conditions for exponential stability as well as prescribed H_∞norm level of the state estimation error system are proposed and verified,and all obtained results are expressed in terms of strict linear matrix inequalities(LMIs).Examples and simulations are presented to show the effectiveness of the proposed methods,at the same time,the effect of leakage delay on stability of neural networks system and on the attenuation level of state estimator are discussed.
基金supported by the National Natural Science Foundation of China under Grant Nos.62173174,61773191,61973148,62003154Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions under Grant No.2019KJI010+2 种基金the Natural Science Foundation of Shandong Province for Outstanding Young Talents in Provincial Universities under Grant No.ZR2016JL025Undergraduate Education Reform Project of higher Education in Shandong Province under Grant No.M2018X047Liaocheng University Education Reform Project Foundation under Grant Nos.G201811,26322170267。
文摘This paper researches the strict dissipative control problem for uncertain fuzzy neutral Markov jump systems by Takagi-Sugeno fuzzy rules.The asynchronous phenomenon is considered between the uncertain fuzzy neutral Markov jump systems modes and asynchronous fuzzy P-D feedback controller modes,which is described by a hidden Markov model.Via using linear matrix inequalities,the desired asynchronous fuzzy P-D feedback controller is obtained,which can ensure that the closed-loop uncertain fuzzy neutral Markov jump systems satisfies robustly exponential mean square stabilization with strict dissipativity.A numerical example and a single-link robot arm are utilized to demonstrate the effectiveness of the method.
基金supported by the National Natural Science Foundation of China(Grant Nos.11971486,11771452)the Natural Science Foundation of Hunan(Grant Nos.2019JJ40357,2020JJ4674).
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.
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.
