本文選題：投資組合 + 跳-擴(kuò)散過程　； 參考：《暨南大學(xué)》2014年碩士論文

【摘要】：在金融投資理論中，，投資組合管理是一個(gè)備受關(guān)注的研究課題，是現(xiàn)代金融工程的重要研究?jī)?nèi)容。而資產(chǎn)-負(fù)債管理又是現(xiàn)代投資組合管理和風(fēng)險(xiǎn)管理的重要研究領(lǐng)域之一，受到越來越多的重視。 Sharpe和Tint(1990)首次將負(fù)債引入到投資組合管理中，研究了負(fù)債情形下的均值-方差投資組合選擇模型，為資產(chǎn)-負(fù)債管理的后續(xù)分析奠定了理論基礎(chǔ)；Xie和Li(2008)等人對(duì)多個(gè)風(fēng)險(xiǎn)資產(chǎn)和一個(gè)負(fù)債在不完全市場(chǎng)下，且具有連續(xù)時(shí)間的均值-方差投資組合選擇模型進(jìn)行了研究，得到了最優(yōu)投資組合策略和均值-方差模型的有效解。 本文是在Xie和Li等人的工作基礎(chǔ)上，在已有的資產(chǎn)模型中加入帶跳部分，研究了跳-擴(kuò)散過程下資產(chǎn)-負(fù)債模型的投資組合問題。 相比于Xie和Li等人的研究方法與思路，本文是基于不完全市場(chǎng)背景下的投資組合研究，使用降維的方法讓不完全市場(chǎng)轉(zhuǎn)化為完全市場(chǎng)；在資產(chǎn)模型中引入跳躍部分，且?guī)S的資產(chǎn)與負(fù)債存在相關(guān)關(guān)系，利用隨機(jī)控制論中的動(dòng)態(tài)規(guī)劃理論并結(jié)合HJB方程，求解出了滿足目標(biāo)函數(shù)的最優(yōu)投資比例和投資組合期望收益，即給出了跳-擴(kuò)散過程下資產(chǎn)-負(fù)債模型的最優(yōu)投資策略和投資組合期望收益的解析表達(dá)式；同時(shí)還考慮了跳-擴(kuò)散過程下基于不同利率的資產(chǎn)-負(fù)債模型，并研究了此類問題的風(fēng)險(xiǎn)管理和最優(yōu)投資組合問題。本文的研究可視為對(duì)資產(chǎn)-負(fù)債管理問題的一個(gè)自然延伸與推廣。
[Abstract]:In the theory of financial investment, portfolio management is a subject of great concern and an important research content of modern financial engineering. Asset-liability management is one of the most important research fields in modern portfolio management and risk management. Sharpe and Tint 1990) introduced debt into portfolio management for the first time, and studied the mean-variance portfolio selection model in the case of debt. It lays a theoretical foundation for the follow-up analysis of asset-liability management, such as Xie and Li, et al., and studies the mean-variance portfolio selection model of multiple risky assets and a liability in incomplete market with continuous time. The optimal portfolio strategy and the efficient solution of the mean-variance model are obtained. In this paper, based on the work of Xie and Li et al., the portfolio problem of asset-liability model in the jump-diffusion process is studied by adding a jump part to the existing asset model. Compared with the research methods and ideas of Xie and Li et al., this paper is based on portfolio research in the context of incomplete market, using dimensionality reduction method to transform incomplete market into complete market, and introducing jump part into asset model. Moreover, there is a correlation between assets with jump and liabilities. By using the dynamic programming theory in stochastic cybernetics and HJB equation, the optimal investment ratio and the expected return of the portfolio are obtained, which satisfy the objective function. The analytical expressions of the optimal investment strategy and the expected return of the portfolio are given, and the asset-liability model based on different interest rates is also considered in the jump-diffusion process. The risk management and optimal portfolio problem of this kind of problems are studied. The study of this paper can be regarded as a natural extension and extension of asset-liability management problem.
【學(xué)位授予單位】：暨南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F224;F830.59

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