Studies On Weighted TVaR As A Kind Of Generalized Convex Risk Measure

Risk management plays a vital role in finance. As the most important part of risk management, risk measurement should be studied. The dissertation investigates the non-linear weighted tail value at risk, which was proposed by Chen and Yang(2011). Generally speaking, investors have different risk aversion towards losses which have different sizes. The main advantage of the new risk measure is that it takes this feature into consideration and describes the difference through weighted functions.In chapter 1, the background and development of risk measures are briefly discussed, including VaR, TVaR, coherent risk measure and convex risk measure. Chapter 2 intro-duces the definition of WTVaR and gives detailed deduction of the corresponding proper-ties. Then, the part of the thesis explains how to select weighted functions and estimate the parameters under different loss distributions. In particular, under the assumption of normal distribution or student-t distribution, the thesis shows the explicit solutions and gives the detailed calculation. Chapter 3 concerns about the estimation of WTVaR when the loss distribution is unknown. The chapter estimates the value of WTVaR through the kernel density non-parameter estimation and the empirical estimation respectively. Then, it compares the effects of the two methods in order to provide theoretical evidence.Chapter 4 and chapter 5 lay particular emphasis on the application of WTVaR. Chapter 4 mainly investigates the application of WTVaR when measuring risks of financial assets. First, taking the pricing model of European call option for instance, WTVaR is used to evaluate risks. Also, under the assumption of GARCH model, the thesis forecasts the one-step-forward relative loss and derives the value of WTVaR. In addition, real data from Shanghai composite index are used to compare WTVaR risk measure with VaR and TVaR risk measures. The results show the advantages of WTVaR that it can not only describe the tail of the loss distribution, but can reflect the risk aversion of investors. Chapter 5 investigates the application of WTVaR from the aspect of optimal portfolio. Considering the significance of short selling, the thesis proposes a programming problem and changes it into a convex programming, which could be solved by computer software.