Worst-case CVaR Rick Measure And Its Applicationa In Portfolio Selection Problems

As the deepening globalization of the economic and finance, the rapid development of the financial information technology as well as a series of theory and practice of financial innovation, the financial market and financial products have a vigorous development trend. However, with the accumulated speed change in social development, all kinds of financial institutions have to deal with a large number of complex risks, which have a major impact on their operation and development. If they lack of effective risk management, not only the financial institutions face more crisis, but also it have the incalculable effects on the whole financial system eve n the society. The financial crisis caused by the US subprime mortgage crisis is the best example. Facing new financial ecological environment, the advanced international financial institutions have established comprehensive risk management system, steadily improve risk management technology and information system, minimize the possible impact and loss. In this context, how to effectively identify, measure, and control the risk has been a big problem in financial institutions of our country.This article explores the worst-case CVa R(WCCVaR) as the risk constraint in robust portfolio optimization problem. The research idea of this paper is: firstly, define the WCCVa R and its mathematical expression; secondly, establish and solve two different single cycle mean-WCCVa R Models by its portfolios whether contains risk- free assets; thirdly, promote up to dynamic programming problem and solve it by the idea of Bellman equation; lastly, test the Model, which proposed by this article, with numerical simulation and real experiment data. Specifically, this paper mainly includes the following six parts:Chapter 1, Introduction, elaborate the research background and significance of this paper firstly. Then, we have a brief overview and comment over the study of scholars at home and abroad about single cycle portfolio model, the combined cycle model and robust portfolio model. Thirdly, we put forward the research ideas and methods. Finally this paper points out the innovation and deficiency.Chapter 2, C Va R and WCC VaR, firstly gives the definition of risk measure and the concept of Va R and C VaR, and gives the consistency of risk measurement should satisfy the four axioms, and then presents a portfolio of CVa R, finally through asset income distribution uncertainty hypothesis, the worst case CVa R portfolio and its parameters is given.Chapter 3, Single cycle mean-WCCVa R portfolio problem, puts forward the assumptions of the Model firstly, then establish two kinds of different Models, which distinguish by whether the portfolio contains risk- free assets, and find the solutions of the Models using the KKT condition, finally compare the above two models.Chapter 4, Mutiple cycles of dynamic portfolio selection problem. O n the basis of the previous chapter, this chapter of single periodic portfolio problem is the focus of this article research content. First of all, we distinguishe whether the portfolio contains risk- free assets, and establish two kinds of dynamic mean-WCCVaR Models. Then we introduce the idea of Bellman equation and solve the dynamic programming problems by it. In multiple cycle problems, this paper considers the assets in different periods of expected return and variance-covariance, and investor risk tolerance in different periods and appetite for risk degree of the influence of different factors such as the model. So many cycles mean-WCCVaR model is more close to reality; its applicability is more extensive. It makes up the defect of the single cycle model.Chapter 5, N umerical tests, includes numerical simulation and real experiment test. In the simulation of numerical experiment, this chapter considers the investor’s risk tolerance, the confidence level and investment cycle for the impact on the value function. Finally, experiment results show that the mean-WCCVaR Model has a stable profitability and ability to resist market shock.Chapter 6, Conclusions and Suggestions, puts forward two suggestions based on previous analysis. Firstly, consider the risk of investment fully. Secondly, consider the difference in risk tolerance and risk preferences of investors.