Cvar-based Dynamic Programming Models And Their Applications In Investment Portfolio

As one of the most important research fields in Economics, Modern Portfolio Theory aims for an optimal investment portfolio, which assures minimum investment risk with expected rates of return, or maximum investment return with fixed risk level. The"risk"here mainly refers to the non-systematic risk, which can be reduced by adjusting the portfolio strategy to ensure the stable income of the investors. Compared to the measurement of return, the measurement of risk is more important and complicated.Two main risk measure methods will be discussed in this thesis, namely, VaR(Value-at-Risk) risk measure method and CVaR(Conditional-Value-at-Risk) risk measure method. In the first place, the definition, property and metering methods of the VaR and CVaR will be introduced. Also, the related model of mean-CVaR will be put forward to discuss its bound and efficient frontier under Normal distribution, and its mathematical statement and graph. In the second part, we propose a dynamic CVaR portfolio model based on dynamic programming method, and put the VaR to constraint conditions innovatively. Setting VaR as the frontier to defend risk is able to avoid the apparent drawback of it as well as to make full use of the advantage of CVaR, which could help to reduce the risk of portfolio effectively. Third, the paper will choose the actual stock data from China's stocks market to make empirical research and calculate the loss of risks and portfolio investment ratio under certain confidence level. Simulation results confirm that the risk of Multi-stage portfolio investment is smaller than that of Single-stage. The conclusion and perspectives are presented at the end of this thesis.