This paper presents an asynchronous output-feed-back control strategy of semi-Markovian systems via sliding mode-based learning technique.Compared with most literature results that require exact prior knowledge of sys...This paper presents an asynchronous output-feed-back control strategy of semi-Markovian systems via sliding mode-based learning technique.Compared with most literature results that require exact prior knowledge of system state and mode information,an asynchronous output-feedback sliding sur-face is adopted in the case of incompletely available state and non-synchronization phenomenon.The holonomic dynamics of the sliding mode are characterized by a descriptor system in which the switching surface is regarded as the fast subsystem and the system dynamics are viewed as the slow subsystem.Based upon the co-occurrence of two subsystems,the sufficient stochastic admissibility criterion of the holonomic dynamics is derived by utilizing the characteristics of cumulative distribution functions.Furthermore,a recursive learning controller is formulated to guarantee the reachability of the sliding manifold and realize the chattering reduction of the asynchronous switching and sliding motion.Finally,the proposed theoretical method is substantia-ted through two numerical simulations with the practical contin-uous stirred tank reactor and F-404 aircraft engine model,respectively.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
This work is concerned with coupling for a class of Markovian switching jump-diffusion processes.The processes under consideration can be regarded as a number of jump-diffusion processes modulated by a Markovian switc...This work is concerned with coupling for a class of Markovian switching jump-diffusion processes.The processes under consideration can be regarded as a number of jump-diffusion processes modulated by a Markovian switching device.For this class of processes,we construct a successful coupling and an order-preserving coupling.展开更多
Our article discusses a class of Jump-diffusion stochastic differential system under Markovian switching(JD-SDS-MS).This model is generated by introducing Poisson process and Markovian switching based on a normal stoc...Our article discusses a class of Jump-diffusion stochastic differential system under Markovian switching(JD-SDS-MS).This model is generated by introducing Poisson process and Markovian switching based on a normal stochastic differential equation.Our work dedicates to analytical properties of solutions to this model.First,we give some properties of the solution,including existence,uniqueness,non-negative and global nature.Next,boundedness of first moment of the solution to this model is considered.Third,properties about coefficients of JD-SDS-MS is proved by using a right continuous markov chain.Last,we study the convergence of Euler-Maruyama numerical solutions and apply it to pricing bonds.展开更多
The main purpose of this thesis is in analyzing and empirically simulating risk minimizing European foreign exchange option pricing and hedging strategy when the spot foreign exchange rate is governed by a Markov-modu...The main purpose of this thesis is in analyzing and empirically simulating risk minimizing European foreign exchange option pricing and hedging strategy when the spot foreign exchange rate is governed by a Markov-modulated jump-diffusion model. The domestic and foreign money market interest rates, the drift and the volatility of the exchange rate dynamics all depend on a continuous-time hidden Markov chain which can be interpreted as the states of a macro-economy. In this paper, we will provide a practical lognormal diffusion dynamic of the spot foreign exchange rate for market practitioners. We employing the minimal martingale measure to demonstrate a system of coupled partial-differential-integral equations satisfied by the currency option price and attain the corresponding hedging schemes and the residual risk. Numerical simulations of the double exponential jump diffusion regime-switching model are used to illustrate the different effects of the various parameters on currency option prices.展开更多
Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies recently.SMJLS is governed by stochastic and deterministic commutations.This paper focuses on the switching strategy wh...Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies recently.SMJLS is governed by stochastic and deterministic commutations.This paper focuses on the switching strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results and investigate new aspects of such systems.Several sufficient conditions for finite-time stability of discrete-time SMJLS are provided,and the numerical problems in these sufficient conditions are solved by solving linear matrix inequalities(LMIs).Finally,numerical examples are given to show the feasibility and effectiveness of the results.展开更多
The authors prove a sufficient stochastic maximum principle for the optimal control of a forward-backward Markov regime switching jump diffusion system and show its connection to dynamic programming principle. The res...The authors prove a sufficient stochastic maximum principle for the optimal control of a forward-backward Markov regime switching jump diffusion system and show its connection to dynamic programming principle. The result is applied to a cash flow valuation problem with terminal wealth constraint in a financial market. An explicit optimal strategy is obtained in this example.展开更多
A parameter estimation method,called PMCMC in this paper,is proposed to estimate a continuous-time model of the term structure of interests under Markov regime switching and jumps.There is a closed form solution to te...A parameter estimation method,called PMCMC in this paper,is proposed to estimate a continuous-time model of the term structure of interests under Markov regime switching and jumps.There is a closed form solution to term structure of interest rates under Markov regime.However,the model is extended to be a CKLS model with non-closed form solutions which is a typical nonlinear and non-Gaussian state-space model(SSM)in the case of adding jumps.Although the difficulty of parameter estimation greatly prevents from researching models,we prove that the nonlinear and non-Gaussian state-space model has better performances in studying volatility.The method proposed in this paper will be implemented in simulation and empirical study for SHIBOR.Empirical results illustrate that the PMCMC algorithm has powerful advantages in tackling the models.展开更多
We investigate periodic solutions of regime-switching jump diffusions.We first show the well-posedness of solutions to stochastic differential equations corresponding to the hybrid system.Then,we derive the strong Fel...We investigate periodic solutions of regime-switching jump diffusions.We first show the well-posedness of solutions to stochastic differential equations corresponding to the hybrid system.Then,we derive the strong Feller property and irreducibility of the associated time-inhomogeneous semigroups.Finally,we establish the existence and uniqueness of periodic solutions.Concrete examples are presented to illustrate the results.展开更多
基金supported in part by the National Science Fund for Excellent Young Scholars of China(62222317)the National Science Foundation of China(62303492)+3 种基金the Major Science and Technology Projects in Hunan Province(2021GK1030)the Science and Technology Innovation Program of Hunan Province(2022WZ1001)the Key Research and Development Program of Hunan Province(2023GK2023)the Fundamental Research Funds for the Central Universities of Central South University(2024ZZTS0116)。
文摘This paper presents an asynchronous output-feed-back control strategy of semi-Markovian systems via sliding mode-based learning technique.Compared with most literature results that require exact prior knowledge of system state and mode information,an asynchronous output-feedback sliding sur-face is adopted in the case of incompletely available state and non-synchronization phenomenon.The holonomic dynamics of the sliding mode are characterized by a descriptor system in which the switching surface is regarded as the fast subsystem and the system dynamics are viewed as the slow subsystem.Based upon the co-occurrence of two subsystems,the sufficient stochastic admissibility criterion of the holonomic dynamics is derived by utilizing the characteristics of cumulative distribution functions.Furthermore,a recursive learning controller is formulated to guarantee the reachability of the sliding manifold and realize the chattering reduction of the asynchronous switching and sliding motion.Finally,the proposed theoretical method is substantia-ted through two numerical simulations with the practical contin-uous stirred tank reactor and F-404 aircraft engine model,respectively.
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.
基金Supported by the National Natural Science Foundation of China (11171024)
文摘This work is concerned with coupling for a class of Markovian switching jump-diffusion processes.The processes under consideration can be regarded as a number of jump-diffusion processes modulated by a Markovian switching device.For this class of processes,we construct a successful coupling and an order-preserving coupling.
基金Supported by the National Natural Science Foundation of China(71471075)Fundamental Research Funds for the Central University(19JNLH09)Humanities and Social Sciences Foundation of Ministry of Education,China(14YJAZH052).
文摘Our article discusses a class of Jump-diffusion stochastic differential system under Markovian switching(JD-SDS-MS).This model is generated by introducing Poisson process and Markovian switching based on a normal stochastic differential equation.Our work dedicates to analytical properties of solutions to this model.First,we give some properties of the solution,including existence,uniqueness,non-negative and global nature.Next,boundedness of first moment of the solution to this model is considered.Third,properties about coefficients of JD-SDS-MS is proved by using a right continuous markov chain.Last,we study the convergence of Euler-Maruyama numerical solutions and apply it to pricing bonds.
基金Supported by the National Natural Science Foundation of China(No.11301454,No.71771147 and No.71201100)the Jiangsu Qing Lan Project for Excellent Young Teachers in University(2014)+1 种基金Six Talent Peaks Project in Jiangsu Province(2016-JY-081)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17KJB110020)
文摘The main purpose of this thesis is in analyzing and empirically simulating risk minimizing European foreign exchange option pricing and hedging strategy when the spot foreign exchange rate is governed by a Markov-modulated jump-diffusion model. The domestic and foreign money market interest rates, the drift and the volatility of the exchange rate dynamics all depend on a continuous-time hidden Markov chain which can be interpreted as the states of a macro-economy. In this paper, we will provide a practical lognormal diffusion dynamic of the spot foreign exchange rate for market practitioners. We employing the minimal martingale measure to demonstrate a system of coupled partial-differential-integral equations satisfied by the currency option price and attain the corresponding hedging schemes and the residual risk. Numerical simulations of the double exponential jump diffusion regime-switching model are used to illustrate the different effects of the various parameters on currency option prices.
基金the National Natural Science Foundation of China(No.61573237)the“111 Project”(No.D18003)the Program of China Scholarship Council(No.201906895021)。
文摘Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies recently.SMJLS is governed by stochastic and deterministic commutations.This paper focuses on the switching strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results and investigate new aspects of such systems.Several sufficient conditions for finite-time stability of discrete-time SMJLS are provided,and the numerical problems in these sufficient conditions are solved by solving linear matrix inequalities(LMIs).Finally,numerical examples are given to show the feasibility and effectiveness of the results.
基金supported by the National Natural Science Foundation of China(No.61573217)the 111 Project(No.B12023)the National High-level Personnel of Special Support Program and the Chang Jiang Scholar Program of the Ministry of Education of China
文摘The authors prove a sufficient stochastic maximum principle for the optimal control of a forward-backward Markov regime switching jump diffusion system and show its connection to dynamic programming principle. The result is applied to a cash flow valuation problem with terminal wealth constraint in a financial market. An explicit optimal strategy is obtained in this example.
基金Supported by National Natural Science Foundation of China(71471075)Fundamental Research Funds for the Central University(19JNLH09)Humanities and Social Sciences Foundation of Ministry of Education,China(14YJAZH052).
文摘A parameter estimation method,called PMCMC in this paper,is proposed to estimate a continuous-time model of the term structure of interests under Markov regime switching and jumps.There is a closed form solution to term structure of interest rates under Markov regime.However,the model is extended to be a CKLS model with non-closed form solutions which is a typical nonlinear and non-Gaussian state-space model(SSM)in the case of adding jumps.Although the difficulty of parameter estimation greatly prevents from researching models,we prove that the nonlinear and non-Gaussian state-space model has better performances in studying volatility.The method proposed in this paper will be implemented in simulation and empirical study for SHIBOR.Empirical results illustrate that the PMCMC algorithm has powerful advantages in tackling the models.
基金The authors thank the referees for the careful reading of their paper and all of the insightful suggestions and comments that greatly improved the presentation of the paper.This work was supported by the research fund from Shanxi Province Department of Finance and Education for Ph.D.Graduates to Work in Shanxi(No.2021-18,125/Z24179)and the Natural Sciences and Engineering Research Council of Canada(No.4394-2018).
文摘We investigate periodic solutions of regime-switching jump diffusions.We first show the well-posedness of solutions to stochastic differential equations corresponding to the hybrid system.Then,we derive the strong Feller property and irreducibility of the associated time-inhomogeneous semigroups.Finally,we establish the existence and uniqueness of periodic solutions.Concrete examples are presented to illustrate the results.
