具有马尔科夫调制参数的投资组合策略研究

发布时间：2018-01-04 08:11

本文关键词：具有马尔科夫调制参数的投资组合策略研究　出处：《西安工程大学》2013年硕士论文　论文类型：学位论文

【摘要】：最优投资组合选择问题是金融数学研究方面的一大主要问题，考虑到实际金融市场中微观经济因素对股票价格会造成很大影响，从而在问题模型中引入Markov参数调制，则使投资组合的选择更加贴近实际。论文主要研究内容就围绕带有Markov参数调制的模型展开，，论文首先研究了基于Markov参数调制的随机LQ控制模型的存贷款利率不同条件下的投资组合选择，然后研究利用Markov参数调制的随机最大值原理解决一类最优投资组合选择策略，最后还拓展研究了一类Markov参数调制模型的未定权益定价与套期保值问题。全文分为以下几章：第一章，介绍了课题的研究背景与选题依据，主要是带有Markov参数调制的投资组合研究的实际意义与研究前景。第二章，介绍了Markov体制转换理论，随机LQ控制，随机最大值原理及推广的Ito公式等研究过程中用到的相关预备知识。第三章，将随机LQ控制推广到系统状态为Markov调制的跳跃-扩散过程情况，利用推广后的随机LQ控制模型解决存贷款利率不同条件下的投资组合选择问题，将投资组合选择问题转化为随机LQ最优控制问题后，利用随机变分法及推广的Riccati方程求得金融市场中存贷款利率不同条件下投资组合选择问题的有效策略。第四章，利用带有Markov调制参数的随机最大值原理解决了一类国际市场的风险敏感投资组合问题，令汇率服从标准Brown运动驱动，且同样考虑实际金融市场的状态因素影响，将系统状态推广为有Markov参数调制的跳跃-扩散过程，应用古典变分法得出推广的随机最大值原理，从而得到最优投资组合选择问题的有效策略。第五章，利用Girsanov定理对Brown运动与连续时间Markov链分别进行测度变换后进行整合得到Q测度，在Q测度下研究了Markov参数调制模型的套期保值与未定权益定价。第六章，总结了论文主要研究内容，并提出有待改进与进一步深入研究的问题。
[Abstract]:The choice of optimal portfolio selection is a major problem in the research of financial mathematics . In the light of the fact that the micro - economic factors in the real financial market have a great impact on the stock price , the choice of the portfolio selection is more close to the reality . The paper firstly studies the portfolio selection under different conditions of the loan interest rate of the stochastic LQ control model based on Markov parameter modulation , and then studies the stochastic maximum principle based on Markov parameter modulation to solve a class of optimal portfolio selection strategies , and finally develops the fixed equity pricing and hedging problem of a class of Markov parameter modulation models . The full text is divided into the following chapters : The first chapter introduces the background of research and selection of topics , and is mainly the practical significance and research prospect of portfolio research with Markov parameter modulation . In chapter 2 , we introduce the relevant preliminary knowledge used in the research of Markov regime switching theory , stochastic LQ control , stochastic maximum principle , and generalization . In the third chapter , the stochastic LQ control is extended to the jump - diffusion process of Markov modulation , and the extended stochastic LQ control model is used to solve the problem of portfolio selection under different conditions of loan interest rate . In chapter 4 , the stochastic maximum principle with Markov modulation parameters is used to solve the problem of risk - sensitive investment in a class of international markets , which makes the exchange rate subject to the standard Brown ' s motion drive , and also considers the influence of the state factors of the actual financial market , promotes the system state into the jump - diffusion process with Markov parameter modulation , and applies the classical variational method to obtain the generalized stochastic maximum principle , thus obtaining the effective strategy of the optimal portfolio selection problem . In the fifth chapter , using Girsanov theorem , we obtain the Q measure after the measure transformation of Brown ' s motion and continuous time Markov chain respectively . Under Q measure , we study the hedging of Markov parameter modulation model and the pricing of uncertain equity . Chapter 6 summarizes the main contents of the thesis , and puts forward some problems to be improved and further researched .

【学位授予单位】：西安工程大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.91;O211.6

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