本文關(guān)鍵詞：CEV過程下含期權(quán)的最優(yōu)投資問題研究　出處：《上海師范大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： CEV過程 期權(quán) 套期保值策略 最優(yōu)策略

【摘要】：隨著金融市場的不斷發(fā)展與完善,很多金融衍生產(chǎn)品,例如：期貨,期權(quán)等等,已經(jīng)成為市場上越來越多人的交易對象,因此,當(dāng)投資對象中含有期權(quán)時如何安排自己的投資和消費是當(dāng)前投資者所面臨的實際問題。本文在CEV的過程下就投資對象中含有期權(quán)時的的一些問題進行了研究,并站在兩種角度,結(jié)合實際情況進行分析,一種是站在個人投資角度進行考慮,另一種是站在企業(yè),本文選取的是保險公司的角度進行分析。 本文在第一章中介紹了投資消費問題和CEV的發(fā)展過程,第二章中介紹了本文模型所要用到的基本預(yù)備知識。 第三章中考慮了含有無風(fēng)險證券,風(fēng)險證券以及以該風(fēng)險證券為標(biāo)的資產(chǎn)的歐式看漲期權(quán)的投資組合的最優(yōu)投資以及消費問題,建立效用最大化模型,應(yīng)用動態(tài)規(guī)劃原理得到了關(guān)于指數(shù)效用函數(shù)下的最優(yōu)投資消費策略,另外還得到了投資者的套期保值策略,并對這兩種策略進行了比較,得到了它們之間的關(guān)系式。接著,在上文的基礎(chǔ)上,繼續(xù)考慮了當(dāng)投資組合中含有多個風(fēng)險證券時的情況,以及進一步考慮了當(dāng)投資時間不確定時的最優(yōu)投資消費問題。 第四章中我們站在保險公司的角度上,研究了保險公司在隨機保費下索賠額服從復(fù)合泊松過程的風(fēng)險模型,通過投資市場上的風(fēng)險證券以及以該風(fēng)險證券為標(biāo)的資產(chǎn)的期權(quán),引用了財富效用函數(shù),建立了最優(yōu)投資問題.并根據(jù)隨機控制理論得到了最大化財富的HJB方程,通過求解模型,得到了公司風(fēng)險資產(chǎn)的配置額,最后對風(fēng)險資產(chǎn)的投資進行數(shù)值模擬. 在第五章的結(jié)論與展望中,給出了本論文還存在的不足和今后要深入研究的方向。
[Abstract]:With the continuous development and improvement of financial market , many financial derivatives , such as futures , options and so on , have become more and more people in the market . Therefore , how to arrange their own investment and consumption is the actual problem faced by the current investors when the investment object contains the options . In the CEV process , we analyze some of the problems in the investment object , one is the point of view of the individual investment , and the other is the enterprise . In this article , the angle of the insurance company is analyzed . In chapter 1 , the paper introduces the development process of investment consumption and CEV , and introduces the basic preliminary knowledge to be used in the second chapter . In the third chapter , we consider the optimal investment and consumption problem of the portfolio of Europe - style call options which contain riskless securities , risk securities and the assets which are the subject assets of the risk securities , and establish the utility maximization model . The optimal investment consumption strategy under the function of the index is obtained by using the dynamic programming principle , and the relation between them is obtained . Then , on the basis of the above , the situation of the investment portfolio with multiple risk securities is considered , and the optimal investment consumption problem when the investment time is uncertain is further considered . In the fourth chapter , we have studied the risk model of the insurance company ' s claim to the compound Poisson process under the stochastic premium . Based on the risk securities on the investment market and the option of taking the risk securities as the target asset , this paper quotes the wealth utility function and establishes the optimal investment problem . According to the stochastic control theory , the HJB equation of maximum wealth is obtained . By solving the model , the allocation amount of the company ' s risk assets is obtained . Finally , the investment of the risk assets is simulated numerically . In the conclusion and prospect of the fifth chapter , the deficiency of this paper and the direction to be further studied in the future are given .

【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F224;F830.91;F840.31

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