本文選題：連續(xù)時間 + 均值-CVaR　； 參考：《南京理工大學》2014年碩士論文

【摘要】：Markowitz均值-方差投資組合理論,開創(chuàng)了以數(shù)理方法研究金融問題的先河,取得了一系列影響深遠的理論與實際應用的成果。數(shù)十年來,無數(shù)學者致力于均值-方差模型的理論拓展與應用研究,極大地豐富和發(fā)展了Markowitz組合選擇理論。 近年來,S. Emmer等研究了基于均值-CaR的連續(xù)時間組合選擇問題,給出了該組合問題的有效前沿等有意義的結(jié)果。但該文只考量了資產(chǎn)價格過程服從幾何布朗運動以及無風險意義下的損失界定。本文擬在S. Emmer等人工作的基礎(chǔ)上,繼續(xù)開展更為深入的探索,即研究基于均值-CVaR的連續(xù)時間組合選擇問題。其中,資產(chǎn)價格過程服從跳一擴散過程以及基于無風險與風險資產(chǎn)組合意義下的損失界定。 首先,分別就股價滿足擴散模型和跳-擴散模型的情形,利用伊藤積分及創(chuàng)新性地構(gòu)造了連續(xù)時間下CVaR的顯示表達式；利用該表達式,構(gòu)建了均值-CVaR模型,考慮到股價所服從的跳-擴散過程,運用matlab給出該模型數(shù)值解結(jié)構(gòu)圖以及最佳投資策略和相對應的有效前沿結(jié)構(gòu)圖。通過與均值-方差模型的對比,顯示其合理性和優(yōu)越性。 其次,研究連續(xù)時間下財富效用-CVaR組合選擇問題。以動態(tài)規(guī)劃方法并輔以拉格朗日乘子法,得到了最優(yōu)投資策略和有效前沿的解析解。
[Abstract]:Markowitz's mean-variance portfolio theory creates the first step in the study of financial problems by mathematical methods and has achieved a series of far-reaching theoretical and practical results. In recent decades, numerous scholars have devoted themselves to the theoretical development and application of mean-variance model, which has greatly enriched and developed Markowitz's combinatorial selection theory. In recent years, S. Emmer and others have studied the continuous time combinatorial selection problem based on mean value (-CaR), and obtained some useful results on the efficient frontier of the combinatorial problem. However, this paper only considers the definition of asset price process from geometric Brownian motion to risk-free loss. Based on the work of S. Emmer et al., this paper intends to further explore the problem of continuous time combination selection based on mean value (-CVaR). Among them, the asset price process service from jump-diffusion process and based on the risk-free and risk-free asset portfolio under the meaning of loss definition. Firstly, for the case that the stock price satisfies the diffusion model and the jump-diffusion model, the display expression of CVaR under continuous time is constructed by using Ito integral and innovatively, and the mean-CVaR model is constructed by this expression. Considering the jump-diffusion process of stock price, the numerical solution structure diagram of the model, the optimal investment strategy and the corresponding efficient frontier structure diagram are given by using matlab. The comparison with the mean-variance model shows its rationality and superiority. Secondly, the problem of wealth utility-CVaR portfolio selection in continuous time is studied. By using dynamic programming method and Lagrange multiplier method, the analytical solution of optimal investment strategy and efficient frontier is obtained.
【學位授予單位】：南京理工大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：F830.59;F224

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本文編號：2064922