Utility Conditional Draw At Risk And Its Application In Portfolio Optimzation

CDaR called conditional drawdown at risk is developed on the basis of CVaR. It is a kind of risk measurement model which is a combination of drawdown function and CVaR. Actually, for a given tolerance parameter, CDaR is the mean of the worst (1-α)%drawdowns. CDaR treats all the drawdowns that beyond a certain threshold equally, that is to say, CDaR is a uniform average. But in real markets, the different drawdowns bring investors the different psychological feelings. In order to make the risk measure model reflect the investors’psychological differences generated by the different drawdowns, we introduce utility function into risk measure area to build a new risk measure model-tility conditional drawdown at risk. Further more, we prove that it is a reasonable risk measure model.This paper consists of six parts. The first part introduces the development of the risk measurement theory. The second chapter introduces CDaR that already exists. Chapter3improves CDaR. It proposes UCDR risk measurement model and defines what UCDaR is. Furthermore, it proves the related properties UCDaR has in detail. Considering the distribution information of random variables is partly known, in Chapter Four we put forward the UCDaR model under the worst condition (WUCDaR for short). The fifth chapter applies some of the data on Chinese stock market to verify the validity and superiority of the new model. The last chapter makes the summary and puts forward prospect.