In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and the...In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and therefore,the foreign exchange rate model is incorporated.Under the allowing of selling and borrowing,the problem of maximizing the expected exponential utility of terminal wealth is studied.By solving the corresponding Hamilton-Jacobi-Bellman equations,the optimal investment strategies and value functions are obtained.Finally,numerical analysis is presented.展开更多
Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S.bankruptcy code,in this paper we follow[44]to revisit the De Finetti dividend control problem under the...Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S.bankruptcy code,in this paper we follow[44]to revisit the De Finetti dividend control problem under the reorganization process and the regulator's intervention documented in U.S.Chapter 11 bankruptcy.We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments.Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem,and hence computations and proofs that are distinct from[44]are needed.To account for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy,the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching.Some explicit expressions of the expected net present values under a double barrier dividend strategy,new to the literature,are established in terms of scale functions.With the help of these expressions,we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies.When the tail of the Lévy measure is log-convex,this optimal double barrier dividend strategy is then verified as the optimal dividend strategy,solving our optimal impulse control problem.展开更多
In recent years,the research focus in insurance risk theory has shifted towards multi-type mixed dividend strategies.However,the practical factors and constraints in financial market transactions,such as interest rate...In recent years,the research focus in insurance risk theory has shifted towards multi-type mixed dividend strategies.However,the practical factors and constraints in financial market transactions,such as interest rates,tax rates,and transaction fees,inevitably impact these strategies.By incorporating appropriate constraints,a multi-type mixed strategy can better simulate real-world transactions.Following the approach of Liu et al.[28],we examine a classical compound Poisson risk model that incorporates the constraints of constant interest rates and a periodic-threshold mixed dividend strategy.In this model,the surplus process of insurance companies is influenced by several factors.These factors include constant interest rates,continuously distributed dividends within intervals(threshold dividend strategy),and dividends at discrete time points(periodic dividend strategy).We derive the piecewise integro-differential equations(IDEs)that describe the expected present value of dividends(EPVDs)until ruin time and the Gerber-Shiu expected discounted penalty function.Furthermore,we provide explicit solutions to these IDEs using an alternative method based on the inverse Laplace transform combined with the Dickson-Hipp operator.This enables us to obtain explicit expressions for the dividend and Gerber-Shiu functions.Additionally,we present examples to illustrate the application of our results.展开更多
In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the stro...In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.展开更多
This paper deals with both the leading train and the following train in a train tracking under a four-aspect fixed autoblock system in order to study the optimum operating strategy for energy saving. After analyzing t...This paper deals with both the leading train and the following train in a train tracking under a four-aspect fixed autoblock system in order to study the optimum operating strategy for energy saving. After analyzing the working principle of the four-aspect fixed autoblock system, an energy-saving control model is created based on the dynamics equation of the Wains. In addition to safety, energy consumption and time error are the main concerns of the model. Based on this model, dynamic speed constraints of the following train are proposed, defined by the leading gain dynamically. At the same time, the static speed constraints defined by the line conditions are also taken into account. The parallel genetic algorithm is used to search the optimum operating strategy. In order to simplify the solving process, the external punishment function is adopted to transform this problem with constraints to the one without constraints. By using the real number coding and the strategy of dividing ramps into three parts, the convergence of GA is accelerated and the length of chromosomes is shortened. The simulation result from a four-aspect fixed autoblock system simulation platform shows that the method can reduce the energy consumption effectively in the premise of ensuring safety and punctuality.展开更多
The time-of-use(TOU)strategy can effectively improve the energy consumption mode of customers,reduce the peak-valley difference of load curve,and optimize the allocation of energy resources.This study presents an Opti...The time-of-use(TOU)strategy can effectively improve the energy consumption mode of customers,reduce the peak-valley difference of load curve,and optimize the allocation of energy resources.This study presents an Optimal guidance mechanism of the flexible load based on strategies of direct load control and time-of-use.First,this study proposes a period partitioning model,which is based on a moving boundary technique with constraint factors,and the Dunn Validity Index(DVI)is used as the objective to solve the period partitioning.Second,a control strategy for the curtailable flexible load is investigated,and a TOU strategy is utilized for further modifying load curve.Third,a price demand response strategy for adjusting transferable load is proposed in this paper.Finally,through the case study analysis of typical daily flexible load curve,the efficiency and correctness of the proposed method and model are validated and proved.展开更多
As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initiall...As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12301603).
文摘In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and therefore,the foreign exchange rate model is incorporated.Under the allowing of selling and borrowing,the problem of maximizing the expected exponential utility of terminal wealth is studied.By solving the corresponding Hamilton-Jacobi-Bellman equations,the optimal investment strategies and value functions are obtained.Finally,numerical analysis is presented.
基金the financial support from the National Natural Science Foundation of China(12171405 and 11661074)the Program for New Century Excellent Talents in Fujian Province University+2 种基金the financial support from the Characteristic&Preponderant Discipline of Key Construction Universities in Zhejiang Province(Zhejiang Gongshang University-Statistics)Collaborative Innovation Center of Statistical Data Engineering Technology&ApplicationDigital+Discipline Construction Project(SZJ2022B004)。
文摘Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S.bankruptcy code,in this paper we follow[44]to revisit the De Finetti dividend control problem under the reorganization process and the regulator's intervention documented in U.S.Chapter 11 bankruptcy.We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments.Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem,and hence computations and proofs that are distinct from[44]are needed.To account for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy,the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching.Some explicit expressions of the expected net present values under a double barrier dividend strategy,new to the literature,are established in terms of scale functions.With the help of these expressions,we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies.When the tail of the Lévy measure is log-convex,this optimal double barrier dividend strategy is then verified as the optimal dividend strategy,solving our optimal impulse control problem.
基金supported by the National Natural Science Foundation of China(12361095)the Jiangxi Provincial Natural Science Foundation(20232BAB201028)。
文摘In recent years,the research focus in insurance risk theory has shifted towards multi-type mixed dividend strategies.However,the practical factors and constraints in financial market transactions,such as interest rates,tax rates,and transaction fees,inevitably impact these strategies.By incorporating appropriate constraints,a multi-type mixed strategy can better simulate real-world transactions.Following the approach of Liu et al.[28],we examine a classical compound Poisson risk model that incorporates the constraints of constant interest rates and a periodic-threshold mixed dividend strategy.In this model,the surplus process of insurance companies is influenced by several factors.These factors include constant interest rates,continuously distributed dividends within intervals(threshold dividend strategy),and dividends at discrete time points(periodic dividend strategy).We derive the piecewise integro-differential equations(IDEs)that describe the expected present value of dividends(EPVDs)until ruin time and the Gerber-Shiu expected discounted penalty function.Furthermore,we provide explicit solutions to these IDEs using an alternative method based on the inverse Laplace transform combined with the Dickson-Hipp operator.This enables us to obtain explicit expressions for the dividend and Gerber-Shiu functions.Additionally,we present examples to illustrate the application of our results.
基金the National Natural Science Foundation of China(10571092)the major program of Key Research Institute of HumanitiesSocial Sciences at Universities(04JJD790006).
文摘In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.
基金supported by the National Science & Technology Pillar Program during the Eleventh Five-Year Plan Period of China (No.2009BAG12A05)
文摘This paper deals with both the leading train and the following train in a train tracking under a four-aspect fixed autoblock system in order to study the optimum operating strategy for energy saving. After analyzing the working principle of the four-aspect fixed autoblock system, an energy-saving control model is created based on the dynamics equation of the Wains. In addition to safety, energy consumption and time error are the main concerns of the model. Based on this model, dynamic speed constraints of the following train are proposed, defined by the leading gain dynamically. At the same time, the static speed constraints defined by the line conditions are also taken into account. The parallel genetic algorithm is used to search the optimum operating strategy. In order to simplify the solving process, the external punishment function is adopted to transform this problem with constraints to the one without constraints. By using the real number coding and the strategy of dividing ramps into three parts, the convergence of GA is accelerated and the length of chromosomes is shortened. The simulation result from a four-aspect fixed autoblock system simulation platform shows that the method can reduce the energy consumption effectively in the premise of ensuring safety and punctuality.
基金supported by open fund of state key laboratory of operation and control of renewable energy&storage systems(China electric power research institute)(No.NYB51202201709).
文摘The time-of-use(TOU)strategy can effectively improve the energy consumption mode of customers,reduce the peak-valley difference of load curve,and optimize the allocation of energy resources.This study presents an Optimal guidance mechanism of the flexible load based on strategies of direct load control and time-of-use.First,this study proposes a period partitioning model,which is based on a moving boundary technique with constraint factors,and the Dunn Validity Index(DVI)is used as the objective to solve the period partitioning.Second,a control strategy for the curtailable flexible load is investigated,and a TOU strategy is utilized for further modifying load curve.Third,a price demand response strategy for adjusting transferable load is proposed in this paper.Finally,through the case study analysis of typical daily flexible load curve,the efficiency and correctness of the proposed method and model are validated and proved.
基金supported by the National Natural Science Foundation of China(No.72071202)the Key Laboratory of Mathematics and Engineering Applications,Ministry of Education。
文摘As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.
