含公共开支的R&D经济增长模型

本文讨论了含公共开支的经济增长模型,避免了对生产函数的不恰当的假设,生产函数的形式是很一般的,因此经济系统是复杂的,但通过精巧的数学方法,得到确定的均衡点,并且给出解为正的充分条件.最后,分析了系统的动态性质,给出了经济沿稳定流形收敛于均衡点的条件.     

含公共开支的R&D经济增长模型

本文讨论了含公共开支的经济增长模型,避免了对生产函数的不恰当的假设,生产函数的形式是很一般的,因此经济系统是复杂的,但通过精巧的数学方法,得到确定的均衡点,并且给出解为正的充分条件.最后,分析了系统的动态性质,给出了经济沿稳定流形收敛于均衡点的条件.     

含公共开支的R&D经济增长模型(英文)

本文讨论了含公共开支的经济增长模型 ,避免了对生产函数的不恰当的假设 ,生产函数的形式是很一般的 ,因此经济系统是复杂的 ,但通过精巧的数学方法 ,得到确定的均衡点 ,并且给出解为正的充分条件。最后 ,分析了系统的动态性质 ,给出了经济沿稳定流形收敛于均衡点的条件     

线性脉冲控制系统的能控性与最优控制

首先讨论了一类线性随机脉冲控制系统的精确能控性质,给出了该类控制系统的脉冲精确能控的等价的代数判据.然后提出了一个确定性的二维线性脉冲控制系统的时间-脉冲强度最优控制问题;利用动态规划原理,给出了脉冲最优控制的反馈形式和值函数的显式表达式;说明了值函数在整个平面上是连续的,在左右两个半平面的内部还是连续可微的.     

带有模糊约束的房地产投资随机期望值模型

基于可信性理论,提出一类新的带有模糊约束的房地产投资随机期望值模型来处理房地产经济中的不确定性信息.另一方面,通过目标函数和可信性函数的一些性质将提出的房地产投资问题转化为一个等价的线性形式,从而可以利用经典的线性规划算法进行求解.最后,给出一个房地产投资问题的实例并通过Lindo软件进行求解.     

风险的动态定量和一个相关的随机对策问题

本文讨论不完全市场中股票收益率不确定时的动态风险度量问题和一个相关的随机对策问题。该动态风险度量可表示为一个随机最优控制问题的值函数,以倒向随机微分方程为工具我们给出了最优目标具有的形式,并给出随机对策问题上值与下值相等的充分条件和鞍点的存在性。     

双无限随机环境中的常返马氏链

对双无限随机环境中的马氏链,给出了常返的两种可能的定义,讨论了它们间的联系和基本性质,给出了状态或链为常返的判断准则.讨论了双无限随机环境中马氏链的不变测度的存在性,首次给出了双无限随机环境中马氏链的正常返及零常返的概念,并讨论了其相关性质.特别地,应用不变函数的性质,给出了状态具有正常返性或零常返性的判断准则.     

多面体区域上非光滑函数的迹

本文给出了一类非光滑函数在多面体区域边界上的迹的定义,研究了它们的性质并给出了它们的结构形式.     

随机环境中分枝过程灭绝概率的性质

本文给出了随机环境中分枝过程概率母函数以及灭绝概率的性质.     

正相依风险下离散模型的最优分红

将保险公司各期净损失相互独立的假定改进为依随机序正相依.在相依风险下,利用动态规划原理和状态空间约简,刻画了最优分红策略,证明了区域策略最优,同时讨论了值函数的性质,并给出了数值算法.其中,对涉及独立假定的结论,给出了相依条件下的相应结果,对未涉及独立假定的部分结论也做了改进.研究发现,与独立情形不同,在依随机序正相依风险下,保险公司不必以概率1破产.     

A unified treatment of maximum principle and dynamic programming in stochastic controls

An optimal stochastic control problem is considered in this paper, where the diffusion coefficient also depends on the control and is possibly degenerate. In addition to the usual adjoint process, a second-order adjoint process is introduced. Some relationships between the value function and the adjoint processes are presented via the “super- and sub-differential” which is related to the viscosity solution, without assuming the smoothness of the value function. The maximum principle, dynamic programming and their connections are then established within a unified framework of viscosity solution     

Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem

We study a stochastic optimal control problem for a partially observed diffusion. By using the control randomization method in Bandini et al. (2018), we prove a corresponding randomized dynamic programming principle (DPP) for the value function, which is obtained from a flow property of an associated filter process. This DPP is the key step towards our main result: a characterization of the value function of the partial observation control problem as the unique viscosity solution to the corresponding dynamic programming Hamilton–Jacobi–Bellman (HJB) equation. The latter is formulated as a new, fully non linear partial differential equation on the Wasserstein space of probability measures. An important feature of our approach is that it does not require any non-degeneracy condition on the diffusion coefficient, and no condition is imposed to guarantee existence of a density for the filter process solution to the controlled Zakai equation. Finally, we give an explicit solution to our HJB equation in the case of a partially observed non Gaussian linear–quadratic model.     

能耗强度与能源结构优化对内生经济增长影响研究

本文在垂直创新模型框架下,将能耗强度和碳减排比例引入生产函数,将人们对气候变化的警惕意识引入效用函数,建立了一个动态的内生低碳经济增长模型。通过求解所建动态优化模型,找到了经济长期均衡增长的最优路径,讨论了能源强度和能源消费结构变化与经济均衡增长的相互关系,分析了各参数对经济最优增长路径的影响,比较了化石能源内部消费结构不变和逐年清洁两种情景下的经济最优增长路径的异同。长期来看,能源强度、二氧化碳减排速率与经济增长率有相互的负向线性关系,缩小反映化石能源内部消费结构的综合碳排放系数对经济增长有促进作用。非化石能源比例越高,低碳技术应用越广泛,研发成果对技术积累的贡献率越大,消费者对当前消费的偏好程度越小,人们对气候变化的警惕意识越强,则越有利于经济的低碳发展。     

基于混合跳扩散模型的最优投资消费和寿险购买策略研究

本文研究在混合跳扩散模型下投资者分别投资于寿险、零息债券和股票时,关于最优投资消费和寿险购买的随机策略问题。通过构造满足混合跳扩散模型的金融市场、保险市场和可容许策略,在CRRA(constant relative risk aversion)效用下,利用动态规划的方法求解了对应的HJB方程,获得了值函数和最优策略的显式表达式。为了探索模型的有效性,本文给出了相对风险厌恶系数的数值分析以及相关参数对最优策略的影响。     

Plongement stochastique des systèmes lagrangiens

We define an operator which extends classical differentiation from smooth deterministic functions to certain stochastic processes. Based on this operator, we define a procedure which associates a stochastic analog to standard differential operators and ordinary differential equations. We call this procedure stochastic embedding. By embedding Lagrangian systems, we obtain a stochastic Euler–Lagrange equation which, in the case of natural Lagrangian systems, is called the embedded Newton equation. This equation contains the stochastic Newton equation introduced by Nelson in his dynamical theory of Brownian diffusions. Finally, we consider a diffusion with a gradient drift, a constant diffusion coefficient and having a probability density function. We prove that a necessary condition for this diffusion to solve the embedded Newton equation is that its density be the square of the modulus of a wave function solution of a linear Schrödinger equation. To cite this article: J. Cresson, S. Darses, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

An infinite horizon stochastic maximum principle for discounted control problem with Lipschitz coefficients

In the present work, a stochastic maximum principle for discounted control of a certain class of degenerate diffusion processes with global Lipschitz coefficient is investigated. The value function is given by a discounted performance functional, leading to a stochastic maximum principle of semi-couple forward–backward stochastic differential equation with non-smooth coefficients. The proof is based on the approximation of the Lipschitz coefficients by smooth ones and the approximation of the infinite horizon adjoint process.     

Anticipating Stochastic Differential Equations of Stratonovich Type

We prove the existence and uniqueness of Stratonovich stochastic differential equations where the coefficients and the initial condition may depend on the whole path of the driving Wiener process. Our main hypothesis is that the diffusion coefficient satisfies the Frobenius condition. The solution is given in terms of solutions of ordinary differential equations and the Wiener process. We use this representation to study properties of the solution. Accepted 3 April 1996     

具有生产性与福利性公共支出的随机内生增长模型

文章建立一个随机内生增长模型来阐明主要政策参数对经济增长与社会福利的影响.若对生产函数、效用函数、偏好及随机干扰作一些特殊的假设,我们证明了主要政策参数的均衡值能被模型参数唯一决定.进一步我们还得到了期望增长率与储蓄的清晰解.文章的最后,我们证明了政府支出直接影响个体决策者的决策:即提高经济增长率将减少福利;反之,增加福利将减少增长率.     

Dynamic asset management with risk-sensitive criterion and non-negative factor constraints: a differential game approach

In this paper, we study continuous time portfolio optimization problem where individual securities are directly affected by economic factors. We consider the risk-sensitive criterion function as is familiar in the robust control literature. This is the natural setting for studying the infinite horizon case of the control problem arising in portfolio optimization. Our result extends earlier works by imposing explicitly the non-negativity constraint on the economic factors. This is achieved by using reflected diffusions. The risk-sensitive control problem with reflected diffusion is then converted into a stochastic differential game. The lower value of this game leads immediately to the desired optimal strategy. Also we prove the existence of unique strong solution to reflected diffusions with bounded measurable drift coefficient which is the first result of its kind for higher dimensional reflected diffusions.     

Invariant Measures for Monotone SPDEs with Multiplicative Noise Term

We study diffusion processes corresponding to infinite dimensional semilinear stochastic differential equations with local Lipschitz drift term and an arbitrary Lipschitz diffusion coefficient. We prove tightness and the Feller property of the solution to show existence of an invariant measure. As an application we discuss stochastic reaction diffusion equations.