一类最优投资随机控制模型的马氏链算法

现代金融经济中的很多问题可以构建成随机控制模型,而随机控制的求解却存在一定的困难.马氏链算法应该是一种有效的求解随机控制问题的数值方法.本文以Claus Munk的工作为基础,针对一类最优投资模型,具体确定了马氏链的转移矩阵并证明其满足算法收敛条件,并用MATLAB语言编成一个程序实现.     

部分信息情形下利率非零时的最优消费投资模型研究

考虑了部分信息情形下市场利率非零时的最优消费投资模型,讨论了相应的最优消费投资策略.最后探讨了当扩散系数可逆且漂移系数服从已知分布时的贝叶斯特例,给出了最优交易策略的明确表达式.     

基于马尔可夫过程的级联供应链的可靠性分析

考虑到缓冲库存和随机到达的因素,假定供应链中企业的修复时间和故障前工作时间服从指数分布且其参数不变.在此基础上,将供应链看作一个马尔可夫过程,通过概率状态方程的方法来求解.为多级串联供应链的可靠性分析提供了科学的分析方法.     

Local stability of stationary states in discounted optimal control systems

This paper presents local optimality and stability conditions for stationary solutions of autonomous optimal control problems with a positive rate of discounting. The conditions do not require the Hamiltonian function to be concave with respect to the state variables. Two examples from optimal economic growth theory are discussed to show that our results can be applied in situations when other known stability conditions fail to be satisfied.Part of this paper was written while the author visited the Faculty of Management at the University of Toronto. Support from SSHRC Grant 410-83-9888 and from Grant P6601 of the Austrian Science Foundation is gratefully acknowledged.     

A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information

The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian motion. It is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian motion. For this type of partial information control, one sufficient (a verification theorem) and one necessary conditions of optimality are proved. The control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable. This work was partially supported by Basic Research Program of China (Grant No. 2007CB814904), National Natural Science Foundation of China (Grant No. 10325101) and Natural Science Foundation of Zhejiang Province (Grant No. Y605478, Y606667)     

治愈率模型在屏蔽数据可靠性分析中的应用研究

针对传统方法中的不足,在引入标准治愈率模型的基础上,提出在屏蔽数据可靠性分析中应用一种扩展的治愈率模型的建模方法;分析证明了利用该方法进行建模分析时仅需对模型作较少的前提假设,在信息不足的情况下能够识别出伴随变量对系统寿命分布的影响,进而有效提高模型估计的稳健性.通过运用基于Gibbs抽样的MCMC方法动态模拟出相关参数后验分布的马尔可夫链,给出随机截尾条件下模型参数的贝叶斯估计;实例分析的结果,证明了该模型在可靠性应用中的直观性与有效性.     

多种风险下研发项目投资决策博弈分析

研发项目代表了高新技术企业的核心竞争力,但是其投资和研发的过程所包含的多种风险可能会造成企业经济上的损失。为了保证竞争优势和收益最大化,企业投资前需要对项目的估值非常的精确,以便在竞争中做出最优投资决策。本文以市场中的两个竞争性企业为例,利用欧式复合期权理论与博弈论,量化了技术风险、商业风险和突发风险等不确定性,在经过了信息披露过程之后,分析了市场中企业自身和竞争者的投资决策,建立相应的研发项目投资决策数学模型,对企业的研发项目投资时机和决策收益进行评估,通过博弈得到纳什均衡下的企业最优投资决策。     

Performance Analysis of a Fluid Production/Inventory Model with State-dependence

We study the long-run average performance of a fluid production/ inventory model which alternates between ON periods and OFF periods. During ON periods of random lengths items are added continuously, at some state-dependent rate, to the inventory. During OFF periods the content decreases (again at some state-dependent rate) back to some basic level. We derive the pertinent reward functionals in closed form. For this analysis the steady-state distributions of the stock level process and its jump counterpart are required. In several examples we use the obtained explicit formulas to maximize the long-run average net revenue numerically.      

A full information pricing problem for the sale of several identical commodities

Summary k commodities of the same kind are for sale in a finite time intervalI, and potential customers arrive according to a Poisson process. It is assumed that no customer may buy more than one unit. The seller has to fix, for eacht I, a price for which he is willing to sell a commodity at timet. This decision is based on the knowledge of the probabilities that a customer appearing at timet will accept a price of at mostx monetary units (for allt I andx > 0). There is no possibility of recall of previous customers. We characterize an optimal price function and the maximal expected gain. Further the relation to the persistency problem of Elfving (1967) is exhibited.

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Zusammenfassung k gleichartige Güter sollen in einem endlichen ZeitintervallI an Kunden verkauft werden, deren Ankunftszeitpunkte einen Poisson-Prozeß bilden. Es wird angenommen, daß kein Kunde mehr als eine Einheit kauft. Der Verkäufer muß für jedest I einen Preis angeben, zu dem er eine Einheit zum Zeitpunktt im Falle einer Nachfrage verkaufen würde. Es wird vorausgesetzt, daß er für jedest I und jedesx>0 die Wahrscheinlichkeit kennt, daß ein zur Zeitt eintreffender Kunde höchstens den Preisx für das Gut akzeptiert; die Möglichkeit, auf frühere Kunden zurückzugreifen, ist ausgeschlossen. Für diese Situation wird eine optimale Preisfunktion sowie der zugehörige maximale erwartete Erlös bestimmt. Ferner wird die Beziehung dieses Modells zu einem verwandten Problem von Elfving (1967) herausgestellt.

     

一类部分信息的随机控制问题的极值原理

在本文中,我们证明了一类部分信息的随机控制问题的极值原理的一个充分条件和一个必要条件.其中,随机控制问题的控制系统是一个由鞅和Brown运动趋动的随机偏微分方程.     

R&D投入、技术溢出及吸收能力与经济增长的空间计量分析

利用我国31个省份2001-2010年的面板数据,使用空间滞后模型(SLM)研究了我国区域RD投入、空间溢出效应及吸收能力对经济增长的影响.研究结果表明我国各省份经济增长之间存在着高度的空间相关性,一个省份的RD投入不仅能够促进本地区的经济增长,还会通过技术溢出促进相邻地区的经济增长,同时一个地区吸收能力越强,其对该地区经济增长的影响也越大.