本文關(guān)鍵詞： 投資組合 部分信息 隨機(jī)LQ控制 泊松過程 Markov體制轉(zhuǎn)換 非線性濾波 HJB方程　出處：《西安工程大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

【摘要】：在現(xiàn)代金融市場(chǎng)中考慮信息對(duì)投資組合的影響是至關(guān)重要的，論文主要內(nèi)容是對(duì)部分信息下的證券投資組合選擇模型的研究。證券的投資本質(zhì)上可以分為風(fēng)險(xiǎn)投資(例如:股票)和無風(fēng)險(xiǎn)投資(例如:債券)，能夠合理分配風(fēng)險(xiǎn)資產(chǎn)和無風(fēng)險(xiǎn)資產(chǎn)投資的比例，使投資者獲得最大的收益，這就是所謂投資者尋找的最優(yōu)投資策略。實(shí)際的投資組合問題中股票價(jià)格所滿足的隨機(jī)微分方程中的漂移系數(shù)往往是不能被直接觀測(cè)到的，投資者觀測(cè)到的僅僅是股票價(jià)格。這就是本文中所說的部分信息。論文主要研究對(duì)象是針對(duì)這種部分信息情況下的投資組合問題進(jìn)行研究。 全文內(nèi)容共分為六章： (1)第一章介紹了部分信息下的投資組合選擇問題的研究現(xiàn)狀及研究意義，并簡(jiǎn)單介紹了本論文所要解決的問題和主要研究?jī)?nèi)容。 (2)第二章主要介紹了在論文研究過程當(dāng)中應(yīng)用到的主要工具，涉及的重要定理、引理和定義。 (3)第三章主要研究了在部分信息下的投資組合問題，其中模型中的股票價(jià)格不僅由布朗運(yùn)動(dòng)驅(qū)動(dòng)，而且受到馬爾科夫調(diào)制參數(shù)的影響，運(yùn)用非線性濾波估計(jì)技術(shù)對(duì)平均收益率進(jìn)行估計(jì)，使其模型轉(zhuǎn)化為完全信息下的模型，考慮指數(shù)和對(duì)數(shù)兩種效用函數(shù)下，運(yùn)用隨機(jī)控制的方法，分別對(duì)其最優(yōu)策略進(jìn)行求解。 (4)第四章主要研究了部分信息下，投資組合效用最大化的問題。其中，風(fēng)險(xiǎn)資產(chǎn)（股票）價(jià)格滿足跳擴(kuò)散過程，此過程中的系數(shù)受馬爾科夫調(diào)制參數(shù)的影響。通過運(yùn)用非線性濾波技術(shù)，將部分信息的問題轉(zhuǎn)化為完全信息的問題。最終在均值-方差準(zhǔn)則下計(jì)算出最優(yōu)投資策略。 (5)第五章主要研究的是在部分信息的情況下，股票價(jià)格不僅由布朗運(yùn)動(dòng)驅(qū)動(dòng)，而且受到泊松過程的驅(qū)動(dòng)。對(duì)于不可觀測(cè)的信息，運(yùn)用非線性濾波估計(jì)技術(shù)對(duì)平均收益率進(jìn)行估計(jì)，，并且給出了具體表達(dá)形式。最后，運(yùn)用隨機(jī)LQ控制的方法，對(duì)投資組合問題的最優(yōu)策略進(jìn)行求解。 (6)第六章主要是對(duì)全文進(jìn)行總結(jié)，以及給出今后研究工作的方向。
[Abstract]:It is essential to consider the impact of information on the portfolio in modern financial markets, The main content of this paper is to study the portfolio selection model under partial information. The investment of securities can be divided into venture capital (for example, stock) and risk-free investment (E. G. bond), which can be allocated reasonably. The ratio of risky assets to risk-free investments, This is called the optimal investment strategy that investors seek. The drift coefficients in stochastic differential equations of stock prices in real portfolio problems are often not directly observed. The investors only observe the stock price. This is part of the information in this paper. The main research object of this paper is to study the portfolio problem under the condition of this kind of partial information. The full text is divided into six chapters:. The first chapter introduces the research status and significance of portfolio selection under partial information, and briefly introduces the problems to be solved and the main research contents in this paper. Chapter 2 mainly introduces the main tools, important theorems, Lemma and definitions applied in the research process. In Chapter 3, we mainly study the portfolio problem under partial information, in which the stock price in the model is not only driven by Brownian motion, but also influenced by Markov modulation parameters. The nonlinear filter estimation technique is used to estimate the average rate of return, and the model is transformed into a model with complete information. Considering the exponential and logarithmic utility functions, the optimal strategy is solved by using the stochastic control method. Chapter 4th mainly studies the problem of portfolio utility maximization under partial information. The coefficients in this process are influenced by Markov modulation parameters. By using nonlinear filtering technique, the problem of partial information is transformed into a problem of complete information. Finally, the optimal investment strategy is calculated under the mean-variance criterion. Chapter 5th focuses on the case of partial information, where stock prices are driven not only by Brownian motion, but also by Poisson processes. The nonlinear filter estimation technique is used to estimate the average return rate, and the concrete expression is given. Finally, the optimal strategy of the portfolio problem is solved by using the stochastic LQ control method. Chapter 6th summarizes the full text and gives the direction of future research.
【學(xué)位授予單位】：西安工程大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F830.91;O211.6

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