本文關(guān)鍵詞： CEV模型 OU模型 線性二次控制 動態(tài)規(guī)劃 最優(yōu)策略解 合作微分博弈 非合作微分博弈 主從微分博弈 EAR(在險收 益值)和CAR(在險資本值)　出處：《中南大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

【摘要】：數(shù)理金融是用數(shù)學(xué)的方法來研究金融衍生品的新型學(xué)科,投資組合選擇是其中一個重要研究課題。在現(xiàn)實世界中,投資者所選擇的策略往往需要顧及市場上其他投資者采用的策略。在這種策略選擇相互影響的環(huán)境下尋找最優(yōu)策略,可視為一種博弈行為,因而可以應(yīng)用博弈理論進行研究。此外,投資者在不同時間往往采用不同的策略,即投資策略是一種動態(tài)策略,因此應(yīng)用隨機微分博弈的理論和方法對多個投資者的動態(tài)投資決策問題進行刻畫和求解無疑是一種合適的選擇。 本文首先在前兩章中介紹了文中所要用到的基本理論和基本知識,然后在第三章中分別對股票價格服從CEV過程和OU過程的情形討論了相應(yīng)的投資組合最優(yōu)化的動態(tài)微分博弈問題。應(yīng)用線性二次控制和線性規(guī)劃方法,得到了相應(yīng)博弈問題的最優(yōu)策略和最優(yōu)值函數(shù)。在第四章中對石油公司之間有合作和無合作的情形,研究石油開采的博弈問題和兩個寡頭石油公司之間油價競爭的博弈問題。此外,考慮到石油開采存在先后次序,我們也討論了對應(yīng)的主從博弈問題。在最后一章,對上市的石油公司,采用在險收益值和在險資本值分別作為風(fēng)險度量,研究了最優(yōu)投資組合問題,給出了相應(yīng)的最優(yōu)投資組合及財富的最大期望值。
[Abstract]:Mathematical finance is a new discipline using mathematical method to study the financial derivatives, portfolio selection is one of the important research topic. In the real world, investors choose strategies often need to take into account other investors use on the market strategy in which influence environment to find the optimal strategy can be regarded as a the game behavior, which can be studied by game theory. In addition, investors often use different strategies in different time, the investment strategy is a dynamic strategy, so the application of the theory and method of stochastic differential game to describe and solve the dynamic investment decision-making problem of many investors is undoubtedly an appropriate choice.
In the beginning of the two chapter introduces the basic theory used in this paper and the basic knowledge, and then in the third chapter on the stock price follows the CEV process and OU process is discussed dynamic differential game problem portfolio optimization of the corresponding application. Two linear control and linear programming method, the optimal the optimal strategy and the corresponding game problem of value function. In the fourth chapter of the cooperation between oil companies and non cooperative situation, the price competition between the game game theory in oil exploitation and two oligarch oil company. In addition, taking into account the existence of the order of oil exploitation, we also discuss the problem of the corresponding game in the last chapter, the listed oil company, the value and value as a measure of risk capital at risk in the insurance benefits of the optimal portfolio problem, given the corresponding Optimal portfolio and the maximum expected value of wealth.

【學(xué)位授予單位】：中南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F830.9;F416.22;F224.32

【參考文獻】

相關(guān)期刊論文 前1條

1 劉琦;劉國平;劉慶平;;基于風(fēng)險測度CaR_k的最優(yōu)投資組合(英文)[J];數(shù)學(xué)理論與應(yīng)用;2013年01期

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本文編號：1524557