【摘要】：在實際生活中往往會遇到這樣的問題:為達到將來某預定目標,如何確定當前的狀態(tài)和實施戰(zhàn)略,而倒向隨機微分方程恰好是解決這類問題十分重要的方法。同時,倒向隨機微分方程也是研究偏微分方程、隨機控制、計算機科學等領(lǐng)域的有效工具。倒向隨機微分方程現(xiàn)在已成為隨機分析范疇非常重要的分支之一。本文是一篇綜述報告,主要研究一類特殊的倒向隨機微分方程(BSDE)在局部Lipschitz條件下解的存在性及唯一性,以及與之相關(guān)的最優(yōu)控制隨機系統(tǒng)理論——最大值原理。具體內(nèi)容如下:第一章主要介紹倒向隨機微分方程的發(fā)展狀況、研究現(xiàn)狀及理論意義;第二章為本文涉及到的相關(guān)預備知識;第三章研究一特殊類倒向隨機微分方程在局部Lipschitz條件下局部解和全局解的存在性及唯一性;第四章著重探討一類廣義的帶有隨機系數(shù)的Riccati方程解的全局存在性;第五章給出正向和倒向狀態(tài)方程最優(yōu)控制系統(tǒng)的最大值原理;第六章回顧本論文的幾個主要結(jié)論。
[Abstract]:In real life, we often encounter such problems: how to determine the current state and implementation strategy in order to achieve a predetermined goal in the future, and the backward stochastic differential equation is exactly the most important method to solve this kind of problems. At the same time, backward stochastic differential equation is also an effective tool to study partial differential equation, stochastic control, computer science and so on. The backward stochastic differential equation has become one of the most important branches in the category of stochastic analysis. In this paper, we study the existence and uniqueness of the solution of a special backward stochastic differential equation (BSDE) under the local Lipschitz condition, and the related optimal control stochastic system theory, the maximum principle. The main contents are as follows: the first chapter mainly introduces the development of backward stochastic differential equations, the research status and theoretical significance, the second chapter is the related preparatory knowledge involved in this paper; In chapter 3, the existence and uniqueness of local solution and global solution of a special class of backward stochastic differential equations under local Lipschitz conditions are studied, and the global existence of solutions of a class of generalized Riccati equations with stochastic coefficients is discussed in chapter 4. In chapter 5, the maximum principle of forward and backward state equation optimal control systems is given, and the main conclusions of this paper are reviewed in chapter 6.
【學位授予單位】：中國科學技術(shù)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O211.63;O232

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本文編號：2285864