In this paper, we consider the optimal risk sharing problem between two parties in the insurance business: the insurer and the insured. The risk is allocated between the insurer and the insured by setting a deductible...In this paper, we consider the optimal risk sharing problem between two parties in the insurance business: the insurer and the insured. The risk is allocated between the insurer and the insured by setting a deductible and coverage in the insurance contract. We obtain the optimal deductible and coverage by considering the expected product of the two parties' utilities of terminal wealth according to stochastic optimal control theory. An equilibrium policy is also derived for when there are both a deductible and coverage;this is done by modelling the problem as a stochastic game in a continuous-time framework. A numerical example is provided to illustrate the results of the paper.展开更多
In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune.The fractional derivatives are described in the Caputo sense.The solutions derived using ...In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune.The fractional derivatives are described in the Caputo sense.The solutions derived using this method are easy and very accurate.The model is given by its signal flow diagram.Moreover,a simulation of the system by the Simulink of MATLAB is given.The disease-free equilibrium and stability of the equilibrium point are calculated.Formulation of a fractional optimal control for the cancer model is calculated.In addition,to control the system,we propose a novel modification of its model.This modification is based on converting the model to a memristive one,which is a first time in the literature that such idea is used to control this type of diseases.Also,we study the system’s stability via the Lyapunov exponents and Poincare maps before and after control.Fractional order differential equations(FDEs)are commonly utilized to model systems that have memory,and exist in several physical phenomena,models in thermoelasticity field,and biological paradigms.FDEs have been utilized to model the realistic biphasic decline manner of elastic systems and infection of diseases with a slower rate of change.FDEs are more useful than integer-order in modeling sophisticated models that contain physical phenomena.展开更多
The paper analyses time series that exhibit equilibrium states. It analyses the formation of equilibrium and how the system can return to the aforementioned equilibrium. The tool that is used in the aforementioned ana...The paper analyses time series that exhibit equilibrium states. It analyses the formation of equilibrium and how the system can return to the aforementioned equilibrium. The tool that is used in the aforementioned analysis is time optimal control in the phase plane. It is proved that equilibrium state is sustainable if initial state is not too far from the equilibrium as well as control vector is large enough. On the other hand, if initial state is one standard deviation away from equilibrium state, it is proved that equilibrium cannot be reached. It is the same case with control vector. If it is unbounded, time optimal control cannot be applied. The approach that is introduced represents unconventional method of analysing equilibrium in time series.展开更多
In this paper,the pursuit-evasion game with state and control constraints is solved to achieve the Nash equilibrium of both the pursuer and the evader with an iterative self-play technique.Under the condition where th...In this paper,the pursuit-evasion game with state and control constraints is solved to achieve the Nash equilibrium of both the pursuer and the evader with an iterative self-play technique.Under the condition where the Hamiltonian formed by means of Pontryagin’s maximum principle has the unique solution,it can be proven that the iterative control law converges to the Nash equilibrium solution.However,the strong nonlinearity of the ordinary differential equations formulated by Pontryagin’s maximum principle makes the control policy difficult to figured out.Moreover the system dynamics employed in this manuscript contains a high dimensional state vector with constraints.In practical applications,such as the control of aircraft,the provided overload is limited.Therefore,in this paper,we consider the optimal strategy of pursuit-evasion games with constant constraint on the control,while some state vectors are restricted by the function of the input.To address the challenges,the optimal control problems are transformed into nonlinear programming problems through the direct collocation method.Finally,two numerical cases of the aircraft pursuit-evasion scenario are given to demonstrate the effectiveness of the presented method to obtain the optimal control of both the pursuer and the evader.展开更多
A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibri...A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game （but essentially cooperative in some sense） is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.展开更多
A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,...A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,we obtain a family of closed-loop equilibrium strategies via multi-person differential games.This result extends Yong’s work(2017) in the case of stochastic differential equations,where a unique closed-loop equilibrium strategy can be derived under standard conditions(namely,the control cost weighting matrix is uniformly positive definite,and the other weighting coefficients are positive semidefinite).展开更多
We develop an influenza pandemic model with quarantine and treatment, and analyze the dynamics of the model. Analytical results of the model show that, if basic repro- duction number R0 〈 1, the disease-free equilibr...We develop an influenza pandemic model with quarantine and treatment, and analyze the dynamics of the model. Analytical results of the model show that, if basic repro- duction number R0 〈 1, the disease-free equilibrium （DFE） is globally asymptotically stable, if R0〉 1, the disease is uniformly persistent. The model is then extended to assess the impact of three anti-influenza control measures, precaution, quarantine and treat- ment, by re-formulating the model as an optimal control problem. We focus primarily on controlling disease with a possible minimal the systemic cost. Pontryagin＇s maximum principle is used to characterize the optimal levels of the three controls. Numerical sim- ulations of the optimality system, using a set of reasonable parameter values, indicate that the precaution measure is more effective in reducing disease transmission than the other two control measures. The precaution measure should be emphasized.展开更多
植物光合产物分配受环境因子和生物因子的共同影响。为增进对植物对全球变化响应的理解,从植物个体水平与群落/生态系统水平综述了植物光合产物分配的影响因子与影响机理的最新研究进展。植物个体在光照增强及受水分和养分胁迫时,会将...植物光合产物分配受环境因子和生物因子的共同影响。为增进对植物对全球变化响应的理解,从植物个体水平与群落/生态系统水平综述了植物光合产物分配的影响因子与影响机理的最新研究进展。植物个体在光照增强及受水分和养分胁迫时,会将光合产物更多地分配到根系;CO2浓度升高对植物光合产物分配的影响受土壤氮素的制约,植物受氮素胁迫时,CO2浓度升高会促进光合产物更多地分配到根系;反之,对植物光合产物分配没有影响。植物群落/生态系统的光合产物分配对环境因子的响应不敏感;光合产物向根系的分配比例随其生长阶段逐渐降低。功能平衡假说、源汇关系假说和相关生长关系假说分别从环境因子、个体发育和环境因子与个体发育协同作用方面阐述了植物光合产物分配的影响机理。在此基础上,指出了未来拟重点加强的研究方向:1)生态系统尺度的光合产物向呼吸部分的分配研究;2)地下净初级生产力(belowground net primary productivity,BNPP)研究;3)温室和野外条件下及幼苗和成熟林光合产物分配对环境因子响应的比较研究;4)生态系统尺度的多因子控制试验;5)整合环境因子和个体发育对植物光合产物分配格局的影响研究。展开更多
基金supported by the NSF of China(11931018, 12271274)the Tianjin Natural Science Foundation (19JCYBJC30400)。
文摘In this paper, we consider the optimal risk sharing problem between two parties in the insurance business: the insurer and the insured. The risk is allocated between the insurer and the insured by setting a deductible and coverage in the insurance contract. We obtain the optimal deductible and coverage by considering the expected product of the two parties' utilities of terminal wealth according to stochastic optimal control theory. An equilibrium policy is also derived for when there are both a deductible and coverage;this is done by modelling the problem as a stochastic game in a continuous-time framework. A numerical example is provided to illustrate the results of the paper.
基金funded by“Taif University Researchers Supporting Project number(TURSP-2020/160),Taif University,Taif,Saudi Arabia”.
文摘In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune.The fractional derivatives are described in the Caputo sense.The solutions derived using this method are easy and very accurate.The model is given by its signal flow diagram.Moreover,a simulation of the system by the Simulink of MATLAB is given.The disease-free equilibrium and stability of the equilibrium point are calculated.Formulation of a fractional optimal control for the cancer model is calculated.In addition,to control the system,we propose a novel modification of its model.This modification is based on converting the model to a memristive one,which is a first time in the literature that such idea is used to control this type of diseases.Also,we study the system’s stability via the Lyapunov exponents and Poincare maps before and after control.Fractional order differential equations(FDEs)are commonly utilized to model systems that have memory,and exist in several physical phenomena,models in thermoelasticity field,and biological paradigms.FDEs have been utilized to model the realistic biphasic decline manner of elastic systems and infection of diseases with a slower rate of change.FDEs are more useful than integer-order in modeling sophisticated models that contain physical phenomena.
文摘The paper analyses time series that exhibit equilibrium states. It analyses the formation of equilibrium and how the system can return to the aforementioned equilibrium. The tool that is used in the aforementioned analysis is time optimal control in the phase plane. It is proved that equilibrium state is sustainable if initial state is not too far from the equilibrium as well as control vector is large enough. On the other hand, if initial state is one standard deviation away from equilibrium state, it is proved that equilibrium cannot be reached. It is the same case with control vector. If it is unbounded, time optimal control cannot be applied. The approach that is introduced represents unconventional method of analysing equilibrium in time series.
文摘In this paper,the pursuit-evasion game with state and control constraints is solved to achieve the Nash equilibrium of both the pursuer and the evader with an iterative self-play technique.Under the condition where the Hamiltonian formed by means of Pontryagin’s maximum principle has the unique solution,it can be proven that the iterative control law converges to the Nash equilibrium solution.However,the strong nonlinearity of the ordinary differential equations formulated by Pontryagin’s maximum principle makes the control policy difficult to figured out.Moreover the system dynamics employed in this manuscript contains a high dimensional state vector with constraints.In practical applications,such as the control of aircraft,the provided overload is limited.Therefore,in this paper,we consider the optimal strategy of pursuit-evasion games with constant constraint on the control,while some state vectors are restricted by the function of the input.To address the challenges,the optimal control problems are transformed into nonlinear programming problems through the direct collocation method.Finally,two numerical cases of the aircraft pursuit-evasion scenario are given to demonstrate the effectiveness of the presented method to obtain the optimal control of both the pursuer and the evader.
文摘A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game （but essentially cooperative in some sense） is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.
基金supported by National Natural Science Foundation of China (Grant Nos.12025105, 11971334 and 11931011)the Chang Jiang Scholars Program and the Science Development Project of Sichuan University (Grant Nos. 2020SCUNL101 and 2020SCUNL201)。
文摘A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,we obtain a family of closed-loop equilibrium strategies via multi-person differential games.This result extends Yong’s work(2017) in the case of stochastic differential equations,where a unique closed-loop equilibrium strategy can be derived under standard conditions(namely,the control cost weighting matrix is uniformly positive definite,and the other weighting coefficients are positive semidefinite).
文摘We develop an influenza pandemic model with quarantine and treatment, and analyze the dynamics of the model. Analytical results of the model show that, if basic repro- duction number R0 〈 1, the disease-free equilibrium （DFE） is globally asymptotically stable, if R0〉 1, the disease is uniformly persistent. The model is then extended to assess the impact of three anti-influenza control measures, precaution, quarantine and treat- ment, by re-formulating the model as an optimal control problem. We focus primarily on controlling disease with a possible minimal the systemic cost. Pontryagin＇s maximum principle is used to characterize the optimal levels of the three controls. Numerical sim- ulations of the optimality system, using a set of reasonable parameter values, indicate that the precaution measure is more effective in reducing disease transmission than the other two control measures. The precaution measure should be emphasized.
文摘植物光合产物分配受环境因子和生物因子的共同影响。为增进对植物对全球变化响应的理解,从植物个体水平与群落/生态系统水平综述了植物光合产物分配的影响因子与影响机理的最新研究进展。植物个体在光照增强及受水分和养分胁迫时,会将光合产物更多地分配到根系;CO2浓度升高对植物光合产物分配的影响受土壤氮素的制约,植物受氮素胁迫时,CO2浓度升高会促进光合产物更多地分配到根系;反之,对植物光合产物分配没有影响。植物群落/生态系统的光合产物分配对环境因子的响应不敏感;光合产物向根系的分配比例随其生长阶段逐渐降低。功能平衡假说、源汇关系假说和相关生长关系假说分别从环境因子、个体发育和环境因子与个体发育协同作用方面阐述了植物光合产物分配的影响机理。在此基础上,指出了未来拟重点加强的研究方向:1)生态系统尺度的光合产物向呼吸部分的分配研究;2)地下净初级生产力(belowground net primary productivity,BNPP)研究;3)温室和野外条件下及幼苗和成熟林光合产物分配对环境因子响应的比较研究;4)生态系统尺度的多因子控制试验;5)整合环境因子和个体发育对植物光合产物分配格局的影响研究。
