For the activated dynamics of a Brownian particle moving in a confined system with the presence of entropic barriers, this paper investigates a periodic driving and correlations between two noises. Within the two-stat...For the activated dynamics of a Brownian particle moving in a confined system with the presence of entropic barriers, this paper investigates a periodic driving and correlations between two noises. Within the two-state approximation, the explicit expressions of the mean first passage time （MFPT） and the spectral power amplification （SPA） axe obtained, respectively. Based on the numerical computations, it is found that： （i） The MFPT as a function of the noise intensity exhibits a maximum with the positive correlations between two noises （λ〉0）, this maximum for MFPT shows the characteristic of the entropic noise induced stability （ENIS） effect. The intensity A of correlations between two noises can enhance the ENIS effect. （ii） The SPA as a function of the noise intensity exhibits a double-peak by tuning the noise correlation intensity λ, i.e., the existence of a double-peak behaviour is the identifying characteristic of the double entropic stochastic resonance phenomenon.展开更多
A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transforma...A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.展开更多
This paper studied a supervisory control system for a hybrid off-highway electric vehicle under the chargesustaining(CS)condition.A new predictive double Q-learning with backup models(PDQL)scheme is proposed to optimi...This paper studied a supervisory control system for a hybrid off-highway electric vehicle under the chargesustaining(CS)condition.A new predictive double Q-learning with backup models(PDQL)scheme is proposed to optimize the engine fuel in real-world driving and improve energy efficiency with a faster and more robust learning process.Unlike the existing“model-free”methods,which solely follow on-policy and off-policy to update knowledge bases(Q-tables),the PDQL is developed with the capability to merge both on-policy and off-policy learning by introducing a backup model(Q-table).Experimental evaluations are conducted based on software-in-the-loop(SiL)and hardware-in-the-loop(HiL)test platforms based on real-time modelling of the studied vehicle.Compared to the standard double Q-learning(SDQL),the PDQL only needs half of the learning iterations to achieve better energy efficiency than the SDQL at the end learning process.In the SiL under 35 rounds of learning,the results show that the PDQL can improve the vehicle energy efficiency by 1.75%higher than SDQL.By implementing the PDQL in HiL under four predefined real-world conditions,the PDQL can robustly save more than 5.03%energy than the SDQL scheme.展开更多
This paper deals with the time evolution of information entropy for a stochastic system with double singularities driven by quasimonochromatic noise. The dimension of the Fokker Planck equation is reduced by the linea...This paper deals with the time evolution of information entropy for a stochastic system with double singularities driven by quasimonochromatic noise. The dimension of the Fokker Planck equation is reduced by the linear transfor- mation. The exact expression of the time dependence of information entropy is obtained based on the definition of Shannon＇s information entropy. The relationships between the properties of dissipative parameters, system singularity strength parameter, quasimonochromatic noise, and their effects on information entropy are discussed.展开更多
Aiming at the dimension disaster problem, poor model generalization ability and deadlock problem in special obstacles environment caused by the increase of state information in the local path planning process of mobil...Aiming at the dimension disaster problem, poor model generalization ability and deadlock problem in special obstacles environment caused by the increase of state information in the local path planning process of mobile robot, this paper proposed a Double BP Q-learning algorithm based on the fusion of Double Q-learning algorithm and BP neural network. In order to solve the dimensional disaster problem, two BP neural network fitting value functions with the same network structure were used to replace the two <i>Q</i> value tables in Double Q-Learning algorithm to solve the problem that the <i>Q</i> value table cannot store excessive state information. By adding the mechanism of priority experience replay and using the parameter transfer to initialize the model parameters in different environments, it could accelerate the convergence rate of the algorithm, improve the learning efficiency and the generalization ability of the model. By designing specific action selection strategy in special environment, the deadlock state could be avoided and the mobile robot could reach the target point. Finally, the designed Double BP Q-learning algorithm was simulated and verified, and the probability of mobile robot reaching the target point in the parameter update process was compared with the Double Q-learning algorithm under the same condition of the planned path length. The results showed that the model trained by the improved Double BP Q-learning algorithm had a higher success rate in finding the optimal or sub-optimal path in the dense discrete environment, besides, it had stronger model generalization ability, fewer redundant sections, and could reach the target point without entering the deadlock zone in the special obstacles environment.展开更多
Deep stochastic configuration networks(DSCNs)produce redundant hidden nodes and connections during training,which complicates their model structures.Aiming at the above problems,this paper proposes a double pruning st...Deep stochastic configuration networks(DSCNs)produce redundant hidden nodes and connections during training,which complicates their model structures.Aiming at the above problems,this paper proposes a double pruning structure design algorithm for DSCNs based on mutual information and relevance.During the training process,the mutual information algorithm is used to calculate and sort the importance scores of the nodes in each hidden layer in a layer-by-layer manner,the node pruning rate of each layer is set according to the depth of the DSCN at the current time,the nodes that contribute little to the model are deleted,and the network-related parameters are updated.When the model completes the configuration procedure,the correlation evaluation strategy is used to sort the global connection weights and delete insignificance connections;then,the network parameters are updated after pruning is completed.The experimental results show that the proposed structure design method can effectively compress the scale of a DSCN model and improve its modeling speed;the model accuracy loss is small,and fine-tuning for accuracy restoration is not needed.The obtained DSCN model has certain application value in the field of regression analysis.展开更多
In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol （BVP for short） system with a bounded random parameter...In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol （BVP for short） system with a bounded random parameter. In the analysis, the stochastic BVP system is transformed by the Chebyshev polynomial approximation into an equivalent deterministic system, whose response can be readily obtained by conventional numerical methods. In this way we have explored plenty of stochastic period-doubling bifurcation phenomena of the stochastic BVP system. The numerical simulations show that the behaviour of the stochastic period-doubling bifurcation in the stochastic BVP system is by and large similar to that in the deterministic mean-parameter BVP system, but there are still some featured differences between them. For example, in the stochastic dynamic system the period-doubling bifurcation point diffuses into a critical interval and the location of the critical interval shifts with the variation of intensity of the random parameter. The obtained results show that Chebyshev polynomial approximation is an effective approach to dynamical problems in some typical nonlinear systems with a bounded random parameter of an arch-like probability density function.展开更多
This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rossler system with an arch-like bounded random parameter. First, we transform the stochastic RSssler system into its equiva...This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rossler system with an arch-like bounded random parameter. First, we transform the stochastic RSssler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic RSssler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Rossler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rossler system.展开更多
Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing sys...Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally, numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations.展开更多
The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing-van der Pol system with bounded random parameter of exponential pr...The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing-van der Pol system with bounded random parameter of exponential probability density function subjected to a harmonic excitation. Firstly the stochastic system is reduced into its equivalent deterministic one, and then the responses of stochastic system can be obtained by numerical methods. Nonlinear dynamical behaviour related to stochastic period-doubling bifurcation and chaos in the stochastic system is explored. Numerical simulations show that similar to its counterpart in deterministic nonlinear system of stochastic period-doubling bifurcation and chaos may occur in the stochastic Duffing-van der Pol system even for weak intensity of random parameter. Simply increasing the intensity of the random parameter may result in the period-doubling bifurcation which is absent from the deterministic system.展开更多
The authors consider a compound Cox model of insurance risk with the additional economic assumption of a positive interest rate. As the authors note a duality result relating a compound Cox model of insurance risk wit...The authors consider a compound Cox model of insurance risk with the additional economic assumption of a positive interest rate. As the authors note a duality result relating a compound Cox model of insurance risk with a positive interest rate and a double shot noise process, the authors analyze a double shot noise process systematically for its theoretical distributional properties, based on the piecewise deterministic Markov process theory, and the martingale methodology. The authors also obtain the moments of aggregate accumulated/discounted claims where the claim arrival process follows a Cox process with shot noise intensity. Removing the parameters in a double shot noise process gradually, the authors show that it becomes a compound Cox process with shot noise intensity, a single shot noise process and a compound Poisson process. Numerical comparisons are shown between the moments （i.e. means and variances） of a compound Poisson model and their counterparts of a compound Cox model with/without considering a positive interest rate. For that purpose, the authors assume that claim sizes and primary event sizes follow an exponential distribution, respectively.展开更多
This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the prob...This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method.展开更多
The present article is devoted to nonlinear stochastic partial differential equations with double reflecting walls driven by possibly degenerate,multiplicative noise.We prove that the corresponding Markov semigroup po...The present article is devoted to nonlinear stochastic partial differential equations with double reflecting walls driven by possibly degenerate,multiplicative noise.We prove that the corresponding Markov semigroup possesses an exponentially attracting invariant measure through asymptotic coupling,in which Foias-Prodi estimation and the truncation technique are crucial for the realization of the Girsanov transform.展开更多
In the data envelopment analysis(DEA)literature,productivity change captured by the Malmquist productivity index,especially in terms of a deterministic environment and stochastic variability in inputs and outputs,has ...In the data envelopment analysis(DEA)literature,productivity change captured by the Malmquist productivity index,especially in terms of a deterministic environment and stochastic variability in inputs and outputs,has been somewhat ignored.Therefore,this study developed a firm-specific,DEA-based Malmquist index model to examine the efficiency and productivity change of banks in a stochastic environment.First,in order to estimate bank-specific efficiency,we employed a two-stage double bootstrap DEA procedure.Specifically,in the first stage,the technical efficiency scores of banks were calculated by the classic DEA model,while in the second stage,the double bootstrap DEA model was applied to determine the effect of the contextual variables on bank efficiency.Second,we applied a two-stage procedure for measuring productivity change in which the first stage included the estimation of stochastic technical efficiency and the second stage included the regression of the estimated efficiency scores on a set of explanatory variables that influence relative performance.Finally,an empirical investigation of the Iranian banking sector,consisting of 120 bank-year observations of 15 banks from 2014 to 2021,was performed to measure their efficiency and productivity change.Based on the findings,the explanatory variables(i.e.,the nonperforming loan ratio and the number of branches)indicated an inverse relationship with stochastic technical efficiency and productivity change.The implication of the findings is that,in order to improve the efficiency and productivity of banks,it is important to optimize these factors.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
In this paper,the problem of trajectory de-sign of unmanned aerial vehicles(UAVs)for maximizing the number of satisfied users is studied in a UAV based cellular network where the UAV works as a flying base station tha...In this paper,the problem of trajectory de-sign of unmanned aerial vehicles(UAVs)for maximizing the number of satisfied users is studied in a UAV based cellular network where the UAV works as a flying base station that serves users,and the user indicates its satis-faction in terms of completion of its data request within an allowable maximum waiting time.The trajectory design is formulated as an optimization problem whose goal is to maximize the number of satisfied users.To solve this problem,a machine learning framework based on double Q-learning algorithm is proposed.The algorithm enables the UAV tofind the optimal trajectory that maximizes the number of satisfied users.Compared to the traditional learning algorithms,such as Q-learning that selects and evaluates the action using the same Q-table,the proposed algorithm can decouple the selection from the evaluation,therefore avoid overestimation which leads to sub-optimal policies.Simulation results show that the proposed algorithm can achieve up to 19.4% and 14.1% gains in terms of the number of satisfied users compared to random algorithm and Q-learning algorithm.展开更多
基金Project supported by Natural Science Foundation of Yunnan Province of China (Grant No. 2010CD031)the National Natural Science Foundation of China (Grant Nos. 50906035,90610035,51066002,and U0937604)
文摘For the activated dynamics of a Brownian particle moving in a confined system with the presence of entropic barriers, this paper investigates a periodic driving and correlations between two noises. Within the two-state approximation, the explicit expressions of the mean first passage time （MFPT） and the spectral power amplification （SPA） axe obtained, respectively. Based on the numerical computations, it is found that： （i） The MFPT as a function of the noise intensity exhibits a maximum with the positive correlations between two noises （λ〉0）, this maximum for MFPT shows the characteristic of the entropic noise induced stability （ENIS） effect. The intensity A of correlations between two noises can enhance the ENIS effect. （ii） The SPA as a function of the noise intensity exhibits a double-peak by tuning the noise correlation intensity λ, i.e., the existence of a double-peak behaviour is the identifying characteristic of the double entropic stochastic resonance phenomenon.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872165)
文摘A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.
基金Project(KF2029)supported by the State Key Laboratory of Automotive Safety and Energy(Tsinghua University),ChinaProject(102253)supported partially by the Innovate UK。
文摘This paper studied a supervisory control system for a hybrid off-highway electric vehicle under the chargesustaining(CS)condition.A new predictive double Q-learning with backup models(PDQL)scheme is proposed to optimize the engine fuel in real-world driving and improve energy efficiency with a faster and more robust learning process.Unlike the existing“model-free”methods,which solely follow on-policy and off-policy to update knowledge bases(Q-tables),the PDQL is developed with the capability to merge both on-policy and off-policy learning by introducing a backup model(Q-table).Experimental evaluations are conducted based on software-in-the-loop(SiL)and hardware-in-the-loop(HiL)test platforms based on real-time modelling of the studied vehicle.Compared to the standard double Q-learning(SDQL),the PDQL only needs half of the learning iterations to achieve better energy efficiency than the SDQL at the end learning process.In the SiL under 35 rounds of learning,the results show that the PDQL can improve the vehicle energy efficiency by 1.75%higher than SDQL.By implementing the PDQL in HiL under four predefined real-world conditions,the PDQL can robustly save more than 5.03%energy than the SDQL scheme.
基金Project supported by the National Natural Science Foundation of China(Grant No.11102132)
文摘This paper deals with the time evolution of information entropy for a stochastic system with double singularities driven by quasimonochromatic noise. The dimension of the Fokker Planck equation is reduced by the linear transfor- mation. The exact expression of the time dependence of information entropy is obtained based on the definition of Shannon＇s information entropy. The relationships between the properties of dissipative parameters, system singularity strength parameter, quasimonochromatic noise, and their effects on information entropy are discussed.
文摘Aiming at the dimension disaster problem, poor model generalization ability and deadlock problem in special obstacles environment caused by the increase of state information in the local path planning process of mobile robot, this paper proposed a Double BP Q-learning algorithm based on the fusion of Double Q-learning algorithm and BP neural network. In order to solve the dimensional disaster problem, two BP neural network fitting value functions with the same network structure were used to replace the two <i>Q</i> value tables in Double Q-Learning algorithm to solve the problem that the <i>Q</i> value table cannot store excessive state information. By adding the mechanism of priority experience replay and using the parameter transfer to initialize the model parameters in different environments, it could accelerate the convergence rate of the algorithm, improve the learning efficiency and the generalization ability of the model. By designing specific action selection strategy in special environment, the deadlock state could be avoided and the mobile robot could reach the target point. Finally, the designed Double BP Q-learning algorithm was simulated and verified, and the probability of mobile robot reaching the target point in the parameter update process was compared with the Double Q-learning algorithm under the same condition of the planned path length. The results showed that the model trained by the improved Double BP Q-learning algorithm had a higher success rate in finding the optimal or sub-optimal path in the dense discrete environment, besides, it had stronger model generalization ability, fewer redundant sections, and could reach the target point without entering the deadlock zone in the special obstacles environment.
基金supported by the National Natural Science Foundation of China(62073006)the Beijing Natural Science Foundation of China(4212032)
文摘Deep stochastic configuration networks(DSCNs)produce redundant hidden nodes and connections during training,which complicates their model structures.Aiming at the above problems,this paper proposes a double pruning structure design algorithm for DSCNs based on mutual information and relevance.During the training process,the mutual information algorithm is used to calculate and sort the importance scores of the nodes in each hidden layer in a layer-by-layer manner,the node pruning rate of each layer is set according to the depth of the DSCN at the current time,the nodes that contribute little to the model are deleted,and the network-related parameters are updated.When the model completes the configuration procedure,the correlation evaluation strategy is used to sort the global connection weights and delete insignificance connections;then,the network parameters are updated after pruning is completed.The experimental results show that the proposed structure design method can effectively compress the scale of a DSCN model and improve its modeling speed;the model accuracy loss is small,and fine-tuning for accuracy restoration is not needed.The obtained DSCN model has certain application value in the field of regression analysis.
基金Project supported by the Major Program of the National Natural Science Foundation of China, China （Grant No 10332030）, the National Natural Science Foundation of China （Grant No 10472091）, and the Graduate Starting Seed Fund of Northwestern Polytechnical University, China （Grant No Z200655）.
文摘In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol （BVP for short） system with a bounded random parameter. In the analysis, the stochastic BVP system is transformed by the Chebyshev polynomial approximation into an equivalent deterministic system, whose response can be readily obtained by conventional numerical methods. In this way we have explored plenty of stochastic period-doubling bifurcation phenomena of the stochastic BVP system. The numerical simulations show that the behaviour of the stochastic period-doubling bifurcation in the stochastic BVP system is by and large similar to that in the deterministic mean-parameter BVP system, but there are still some featured differences between them. For example, in the stochastic dynamic system the period-doubling bifurcation point diffuses into a critical interval and the location of the critical interval shifts with the variation of intensity of the random parameter. The obtained results show that Chebyshev polynomial approximation is an effective approach to dynamical problems in some typical nonlinear systems with a bounded random parameter of an arch-like probability density function.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872165)
文摘This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rossler system with an arch-like bounded random parameter. First, we transform the stochastic RSssler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic RSssler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Rossler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rossler system.
基金Project supported by the National Natural Science Foundation of China(Grant Nos10472091and10332030)
文摘Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally, numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations.
基金Project supported by the National Natural Science Foundation of China （Grants Nos 10472091 and 10332030）.
文摘The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing-van der Pol system with bounded random parameter of exponential probability density function subjected to a harmonic excitation. Firstly the stochastic system is reduced into its equivalent deterministic one, and then the responses of stochastic system can be obtained by numerical methods. Nonlinear dynamical behaviour related to stochastic period-doubling bifurcation and chaos in the stochastic system is explored. Numerical simulations show that similar to its counterpart in deterministic nonlinear system of stochastic period-doubling bifurcation and chaos may occur in the stochastic Duffing-van der Pol system even for weak intensity of random parameter. Simply increasing the intensity of the random parameter may result in the period-doubling bifurcation which is absent from the deterministic system.
文摘The authors consider a compound Cox model of insurance risk with the additional economic assumption of a positive interest rate. As the authors note a duality result relating a compound Cox model of insurance risk with a positive interest rate and a double shot noise process, the authors analyze a double shot noise process systematically for its theoretical distributional properties, based on the piecewise deterministic Markov process theory, and the martingale methodology. The authors also obtain the moments of aggregate accumulated/discounted claims where the claim arrival process follows a Cox process with shot noise intensity. Removing the parameters in a double shot noise process gradually, the authors show that it becomes a compound Cox process with shot noise intensity, a single shot noise process and a compound Poisson process. Numerical comparisons are shown between the moments （i.e. means and variances） of a compound Poisson model and their counterparts of a compound Cox model with/without considering a positive interest rate. For that purpose, the authors assume that claim sizes and primary event sizes follow an exponential distribution, respectively.
基金Supported by the Key Grant Project of Chinese Ministry of Education (NO.309018)National Natural Science Foundation of China (NO.70973104,NO.11171304)Zhejiang Provincial Natural Science Foundation of China (NO.Y6110023)
文摘This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method.
基金supported by the National Natural Science Foundation of China(12071480)the Scientific Research Program Funds of NUDT(22-ZZCX-016)the Hunan Provincial Innovation Foundation for Postgraduate(CX20230003)。
文摘The present article is devoted to nonlinear stochastic partial differential equations with double reflecting walls driven by possibly degenerate,multiplicative noise.We prove that the corresponding Markov semigroup possesses an exponentially attracting invariant measure through asymptotic coupling,in which Foias-Prodi estimation and the truncation technique are crucial for the realization of the Girsanov transform.
文摘In the data envelopment analysis(DEA)literature,productivity change captured by the Malmquist productivity index,especially in terms of a deterministic environment and stochastic variability in inputs and outputs,has been somewhat ignored.Therefore,this study developed a firm-specific,DEA-based Malmquist index model to examine the efficiency and productivity change of banks in a stochastic environment.First,in order to estimate bank-specific efficiency,we employed a two-stage double bootstrap DEA procedure.Specifically,in the first stage,the technical efficiency scores of banks were calculated by the classic DEA model,while in the second stage,the double bootstrap DEA model was applied to determine the effect of the contextual variables on bank efficiency.Second,we applied a two-stage procedure for measuring productivity change in which the first stage included the estimation of stochastic technical efficiency and the second stage included the regression of the estimated efficiency scores on a set of explanatory variables that influence relative performance.Finally,an empirical investigation of the Iranian banking sector,consisting of 120 bank-year observations of 15 banks from 2014 to 2021,was performed to measure their efficiency and productivity change.Based on the findings,the explanatory variables(i.e.,the nonperforming loan ratio and the number of branches)indicated an inverse relationship with stochastic technical efficiency and productivity change.The implication of the findings is that,in order to improve the efficiency and productivity of banks,it is important to optimize these factors.
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 in part by the National Natural Science Foundation of China under Grant 61671086 and Grant 61629101。
文摘In this paper,the problem of trajectory de-sign of unmanned aerial vehicles(UAVs)for maximizing the number of satisfied users is studied in a UAV based cellular network where the UAV works as a flying base station that serves users,and the user indicates its satis-faction in terms of completion of its data request within an allowable maximum waiting time.The trajectory design is formulated as an optimization problem whose goal is to maximize the number of satisfied users.To solve this problem,a machine learning framework based on double Q-learning algorithm is proposed.The algorithm enables the UAV tofind the optimal trajectory that maximizes the number of satisfied users.Compared to the traditional learning algorithms,such as Q-learning that selects and evaluates the action using the same Q-table,the proposed algorithm can decouple the selection from the evaluation,therefore avoid overestimation which leads to sub-optimal policies.Simulation results show that the proposed algorithm can achieve up to 19.4% and 14.1% gains in terms of the number of satisfied users compared to random algorithm and Q-learning algorithm.
