分布鲁棒动态经济学模型及其数值解法

发布时间：2018-04-17 13:10

本文选题：新古典经济增长模型 + 分布鲁棒优化　；参考：《大连理工大学》2014年硕士论文

【摘要】：现代经济理论将经济视为一个动态系统,需要面对不确定性作出合理决策.动态因素包括市场走势随时间产生的变化,例如广义上的消费、投资、劳动力供给和技术创新等,这些因素具有重要的实际意义.如果从广义角度来看上述市场走势因素,那么这种决策问题可以应用到很多其它领域,而不仅仅局限于经济领域.新古典经济增长模型是动态经济学中的经典模型,也是宏观经济学中的重要模型,其相关理论分析了资本积累、人口增长及技术进步对经济增长的作用.从90年代开始,人们研究含有随机性的新古典经济增长模型的各种方法,包括经典的样条逼近和迭代相结合的方法. 随机规划是在不确定参数分布已知情况下的决策模型.在分布未知,并且要求所作决策在最坏的分布情况下最优时,对应的是鲁棒优化和分布鲁棒优化模型.鲁棒优化是在给定不确定集的情况下,对于可能出现的所有情况,约束条件均满足,并且使得最坏情况下的目标函数的函数值最优.分布鲁棒优化方法则是在只知道分布的部分信息,比如一阶矩、二阶矩以及支撑集合信息等,在所有满足条件的分布中找寻满足最坏可能分布的解. 本文将分布鲁棒优化的思想应用于带有休闲选择的新古典经济增长模型之中,利用贝尔曼最优性原则建立分布鲁棒动态规划模型,先由一阶最优性条件推导出欧拉方程,再利用对偶变换将欧拉方程右端的优化问题转化为半无限规划问题后,采用样条逼近和牛顿迭代相结合的思想,利用特殊构造的加权二维三次样条逼近策略函数并用牛顿迭代法求解,最后求得策略函数的数值解.
[Abstract]:Modern economic theory regards economy as a dynamic system and needs to make reasonable decision in the face of uncertainty.Dynamic factors include the changes of market trends over time, such as consumption, investment, labor supply and technological innovation in a broad sense. These factors have important practical significance.If you look at these market movements in a broad sense, this decision problem can be applied to many other areas, not just the economy.Neo-classical economic growth model is a classical model in dynamic economics and an important model in macroeconomics. Its related theories analyze the effects of capital accumulation, population growth and technological progress on economic growth.Since the 1990s, people have studied various methods of neoclassical economic growth model with randomness, including the classical spline approximation and iterative method.Stochastic programming is a decision model when uncertain parameter distribution is known.When the distribution is unknown and the decision is required to be optimal in the worst case, the corresponding robust optimization model and the distributed robust optimization model are obtained.Robust optimization is that the constraint conditions are satisfied for all the possible cases given the uncertain set and the function value of the objective function is optimized in the worst case.The method of robust optimization of distribution is to find out the solution of the worst possible distribution in all the distributions that satisfy the conditions, such as the first moment, the second moment and the support set information, which only know the partial information of the distribution, for example, the first order moment, the second order moment and the support set information.In this paper, the idea of distributed robust optimization is applied to the neoclassical economic growth model with leisure choice, and the distributed robust dynamic programming model is established by using the Berman optimality principle. The Euler equation is derived from the first-order optimality condition.Then the optimization problem at the right end of the Euler equation is transformed into a semi-infinite programming problem by dual transformation, and the idea of combining spline approximation with Newton iteration is adopted.The special weighted two-dimensional cubic spline approximation strategy function is solved by Newton iteration method. Finally, the numerical solution of the strategy function is obtained.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F091.3

【共引文献】