本文關(guān)鍵詞： 隨機(jī)最大值原理 隨機(jī)微分博弈 消費(fèi) 相對(duì)消費(fèi) 合作微分博弈 投資組合　出處：《中南大學(xué)》2014年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：摘要：隨機(jī)最大值原理是解決隨機(jī)最優(yōu)控制問(wèn)題的一種重要方法。它是Pontryagin最大值原理的隨機(jī)版本,而Pontryagin最大值原理是確定性動(dòng)態(tài)系統(tǒng)的最優(yōu)控制理論。博弈理論作為主流經(jīng)濟(jì)學(xué)的重要分析工具之一,其方法和思想已廣泛應(yīng)用于最優(yōu)投資組合理論中。因此,對(duì)具有多個(gè)投資者的最優(yōu)消費(fèi)及投資組合博弈問(wèn)題進(jìn)行系統(tǒng)研究,具有重要的理論及現(xiàn)實(shí)意義。 本文系統(tǒng)研究具有相關(guān)性擴(kuò)散過(guò)程的隨機(jī)最大值原理,以及在投資組合選擇和消費(fèi)中的應(yīng)用。首先,考慮狀態(tài)過(guò)程由相關(guān)布朗運(yùn)動(dòng)所控制的隨機(jī)最大值原理,探討隨機(jī)最大值原理與動(dòng)態(tài)規(guī)劃原理的關(guān)系,并把得到的隨機(jī)最大值原理應(yīng)用于非零和主從投資組合博弈中,得到最優(yōu)投資組合策略和最優(yōu)值函數(shù)的顯式表達(dá)式。然后利用最大值原理研究確定性財(cái)富過(guò)程和隨機(jī)性財(cái)富過(guò)程下的最優(yōu)消費(fèi)問(wèn)題,得到最優(yōu)消費(fèi)策略和值函數(shù)的顯式表達(dá)式,并且對(duì)確定性財(cái)富過(guò)程和隨機(jī)性財(cái)富過(guò)程下最優(yōu)消費(fèi)策略和值函數(shù)進(jìn)行系統(tǒng)比較。最后我們研究既考慮絕對(duì)消費(fèi)又考慮相對(duì)消費(fèi)的最優(yōu)消費(fèi)博弈問(wèn)題,在合作博弈與非合作博弈情形下,分別得到最優(yōu)消費(fèi)和值函數(shù)的顯式表達(dá)式,并通過(guò)數(shù)值計(jì)算比較兩種博弈情形下值函數(shù)的差別。
[Abstract]:Absrtact: stochastic maximum principle is an important method to solve stochastic optimal control problem. It is a random version of Pontryagin maximum principle. Pontryagin maximum principle is the optimal control theory of deterministic dynamic system. Game theory is one of the most important analytical tools in mainstream economics. Its methods and ideas have been widely used in the optimal portfolio theory. Therefore, it is of great theoretical and practical significance to systematically study the optimal consumption and portfolio game problem with multiple investors. In this paper, we study the stochastic maximum principle with correlation diffusion process and its application in portfolio selection and consumption. Firstly, we consider the stochastic maximum principle that the state process is controlled by the correlated Brownian motion. The relationship between the stochastic maximum principle and the dynamic programming principle is discussed, and the obtained stochastic maximum principle is applied to the non-zero sum principal and subordinate portfolio game. The explicit expressions of optimal portfolio strategy and optimal value function are obtained, and then the optimal consumption problem under deterministic wealth process and stochastic wealth process is studied by using the maximum value principle. The explicit expressions of optimal consumption strategy and value function are obtained. And the deterministic wealth process and the stochastic wealth process under the optimal consumption strategy and value function are systematically compared. Finally, we study the optimal consumption game problem considering both absolute consumption and relative consumption. In the case of cooperative game and non-cooperative game, the explicit expressions of optimal consumption and value function are obtained, and the difference of value function between the two games is compared by numerical calculation.
【學(xué)位授予單位】：中南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：F224.32;F830.59;F014.5

【共引文獻(xiàn)】

相關(guān)期刊論文 前3條

1 XING LEI;ZHAO PENG-FEI;Li Yong;;Necessary Maximum Principle of Stochastic Optimal Control with Delay and Jump Diffusion[J];Communications in Mathematical Research;2014年03期

2 邢蕾;;時(shí)滯帶跳隨機(jī)最優(yōu)控制的充分型最大值原理[J];吉林大學(xué)學(xué)報(bào)(理學(xué)版);2012年02期

3 冉啟康;;一類(lèi)部分信息的隨機(jī)控制問(wèn)題的極值原理(英文)[J];應(yīng)用數(shù)學(xué);2009年02期

相關(guān)博士學(xué)位論文 前3條

1 王s，

本文編號(hào)：1462931