本文選題：最優(yōu)資產(chǎn)組合 + 最優(yōu)消費(fèi)資產(chǎn)組合　； 參考：《湘潭大學(xué)》2017年碩士論文

【摘要】：1952年,H.Markowiz[1]發(fā)表的博士論文《Porofolio Selection》奠定了金融數(shù)學(xué)的理論基礎(chǔ).他將均值表示股票的收益,將協(xié)方差表示收益的風(fēng)險(xiǎn),量化了股票市場(chǎng)“差異性”的概念.在金融資產(chǎn)中構(gòu)造一個(gè)最優(yōu)的資產(chǎn)組合,使得代表期望回報(bào)的均值和代表風(fēng)險(xiǎn)的方差達(dá)到最佳的平衡.也就是,給定資產(chǎn)的均值回報(bào),應(yīng)使得資產(chǎn)組合的方差最小;或者說(shuō)是給定資產(chǎn)組合的協(xié)方差,應(yīng)使得資產(chǎn)組合的均值回報(bào)最大.由此,最優(yōu)資產(chǎn)組合理論的研究引起了眾多學(xué)者的興趣,對(duì)經(jīng)典Markowiz資產(chǎn)組合問(wèn)題做了許多進(jìn)一步的拓展和應(yīng)用.考慮到投資者不僅有資產(chǎn)組合活動(dòng),還會(huì)將財(cái)富進(jìn)行消費(fèi).于是,Merton[2]討論了最優(yōu)消費(fèi)投資組合問(wèn)題,并且開(kāi)創(chuàng)了隨機(jī)最優(yōu)控制方法.Merton假設(shè)金融模型時(shí)間連續(xù),從此開(kāi)始了連續(xù)時(shí)間資產(chǎn)組合理論.本文假設(shè)資產(chǎn)價(jià)格的變動(dòng)服從帶泊松跳的分?jǐn)?shù)布朗運(yùn)動(dòng),討論了效用函數(shù)為冪函數(shù)的最優(yōu)資產(chǎn)組合和最優(yōu)消費(fèi)資產(chǎn)組合.首先,在緒論中介紹了資產(chǎn)組合策略的歷史和研究的意義,以及研究的成果.其次,在第二章中,預(yù)備知識(shí)的介紹,主要介紹的是幾類基本的隨機(jī)過(guò)程和隨機(jī)分析中的分?jǐn)?shù)布朗運(yùn)動(dòng).然后,在第三章討論了在假定的金融市場(chǎng)模型中,假設(shè)標(biāo)的資產(chǎn)價(jià)格的變動(dòng)服從帶泊松跳的分?jǐn)?shù)布朗運(yùn)動(dòng),研究了最優(yōu)資產(chǎn)組合中資產(chǎn)的配置比例.具體方法為:建立值函數(shù),使得期末財(cái)富總量最大;運(yùn)用動(dòng)態(tài)規(guī)劃原理,推導(dǎo)出HJB微分方程;最后得到最優(yōu)資產(chǎn)組合的分配策略.此解可以給個(gè)人投資者在投資決策時(shí)提供有利的參考.第四章中,考慮了投資者在投資過(guò)程中的消費(fèi),此時(shí)的值函數(shù)為投資財(cái)富和累積消費(fèi)的最大化.對(duì)最優(yōu)消費(fèi)資產(chǎn)組合的研究可以給投資者在投資消費(fèi)過(guò)程中提供決策建議.最后,在第五章中,將本文的主要研究的工作內(nèi)容與進(jìn)展進(jìn)行了簡(jiǎn)要的總結(jié),并對(duì)接下來(lái)的研究方向進(jìn)行了展望.
[Abstract]:In 1952, H.Markowiz[1]'s doctoral thesis, , laid the theoretical basis for financial mathematics. He expressed the earnings of the stock, expressed the risk of the covariance, quantified the concept of the "difference" in the stock market, and constructed a best portfolio in the financial assets to make the mean value of the expected return. The variance of the representative risk reaches the best balance. That is, the mean return of a given asset should make the variance of the portfolio minimum; or the covariance of a given portfolio should make the average return of the portfolio maximum. Therefore, the study of the optimal portfolio theory has aroused the interest of many scholars and the classical Markowiz capital. The problem of production portfolio has been further expanded and applied. Considering that investors not only have portfolio activities, they will also consume wealth. So, Merton[2] discusses the optimal consumption portfolio problem and creates a stochastic optimal control method.Merton assuming that the financial model is a continuous time, and from then on, the continuous time asset group has been started. In this paper, this paper assumes that the change of asset price obeys the fractional Brown movement with Poisson jump, discusses the optimal portfolio of utility function as power function and the optimal combination of consumption assets. First, in the introduction, the history and significance of the portfolio strategy and the results of research are introduced in the introduction. Secondly, in the second chapter, the preparatory knowledge is prepared. This paper introduces several basic random processes and fractional Brown's motion in random analysis. Then, in the third chapter, we discuss the hypothesis that the change of the price of the underlying asset obeys the fractional Brown movement with Poisson jump, and studies the allocation ratio of the assets in the optimal asset portfolio. The vertical value function makes the total amount of the final wealth maximum; using the dynamic programming principle, the HJB differential equation is derived. Finally, the allocation strategy of the optimal portfolio is obtained. This solution can provide a favorable reference for individual investors to make investment decisions. In the fourth chapter, the consumption of investors in the investment process is considered, and the value function at this time is the investment wealth. The research on the optimal consumption asset portfolio can give investors decision making suggestions in the process of investment and consumption. Finally, in the fifth chapter, a brief summary is made on the work and progress of the main research in this paper, and the research direction of the docking is prospected.

【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224;F830.9

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本文編號(hào)：1855402

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