本文選題：新古典經(jīng)濟(jì)增長(zhǎng)模型 + 分布魯棒優(yōu)化　； 參考：《大連理工大學(xué)》2014年碩士論文

【摘要】：現(xiàn)代經(jīng)濟(jì)理論將經(jīng)濟(jì)視為一個(gè)動(dòng)態(tài)系統(tǒng),需要面對(duì)不確定性作出合理決策.動(dòng)態(tài)因素包括市場(chǎng)走勢(shì)隨時(shí)間產(chǎn)生的變化,例如廣義上的消費(fèi)、投資、勞動(dòng)力供給和技術(shù)創(chuàng)新等,這些因素具有重要的實(shí)際意義.如果從廣義角度來看上述市場(chǎng)走勢(shì)因素,那么這種決策問題可以應(yīng)用到很多其它領(lǐng)域,而不僅僅局限于經(jīng)濟(jì)領(lǐng)域.新古典經(jīng)濟(jì)增長(zhǎng)模型是動(dòng)態(tài)經(jīng)濟(jì)學(xué)中的經(jīng)典模型,也是宏觀經(jīng)濟(jì)學(xué)中的重要模型,其相關(guān)理論分析了資本積累、人口增長(zhǎng)及技術(shù)進(jìn)步對(duì)經(jīng)濟(jì)增長(zhǎng)的作用.從90年代開始,人們研究含有隨機(jī)性的新古典經(jīng)濟(jì)增長(zhǎng)模型的各種方法,包括經(jīng)典的樣條逼近和迭代相結(jié)合的方法. 隨機(jī)規(guī)劃是在不確定參數(shù)分布已知情況下的決策模型.在分布未知,并且要求所作決策在最壞的分布情況下最優(yōu)時(shí),對(duì)應(yīng)的是魯棒優(yōu)化和分布魯棒優(yōu)化模型.魯棒優(yōu)化是在給定不確定集的情況下,對(duì)于可能出現(xiàn)的所有情況,約束條件均滿足,并且使得最壞情況下的目標(biāo)函數(shù)的函數(shù)值最優(yōu).分布魯棒優(yōu)化方法則是在只知道分布的部分信息,比如一階矩、二階矩以及支撐集合信息等,在所有滿足條件的分布中找尋滿足最壞可能分布的解. 本文將分布魯棒優(yōu)化的思想應(yīng)用于帶有休閑選擇的新古典經(jīng)濟(jì)增長(zhǎng)模型之中,利用貝爾曼最優(yōu)性原則建立分布魯棒動(dòng)態(tài)規(guī)劃模型,先由一階最優(yōu)性條件推導(dǎo)出歐拉方程,再利用對(duì)偶變換將歐拉方程右端的優(yōu)化問題轉(zhuǎn)化為半無限規(guī)劃問題后,采用樣條逼近和牛頓迭代相結(jié)合的思想,利用特殊構(gòu)造的加權(quán)二維三次樣條逼近策略函數(shù)并用牛頓迭代法求解,最后求得策略函數(shù)的數(shù)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.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F091.3

【共引文獻(xiàn)】

相關(guān)博士學(xué)位論文 前2條

1 朱柏松;基于DSGE模型的貨幣政策和財(cái)政政策聯(lián)動(dòng)機(jī)制研究[D];華中科技大學(xué);2013年

2 鄧郁凡;主權(quán)債務(wù)危機(jī)[D];南開大學(xué);2013年

相關(guān)碩士學(xué)位論文 前1條

1 劉文倩;技術(shù)沖擊、貨幣政策與金融生態(tài)系統(tǒng)的DSGE模型及應(yīng)用研究[D];廈門大學(xué);2014年

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本文編號(hào)：1763741