A Conditional Value At Risk Model Based On Genetic Algorithm

The value at risk (VaR) is a statistic method to measure the risk of stock markets or portfolio, and the conditional value at risk (CVaR) is another kind of statistic method to measure the risk of portfolio, and it measures the risk by calculating the mean of the values which exceed the VaR. CVaR overcomes several limitations of VaR and has good properties, especially its good computability.The research on CVaR mainly focuses on discrete type of CVaR and continuous type of CVaR. This thesis studies continuous type of CVaR based on the methods of systems theory, induction and deduction, comparison and empirical analysis etc.The thesis is organized as follows. In Chapter 1, we introduce the background and the concepts of VaR, CVaR and genetic algorithms. In Chapter 2, we introduce the research status on VaR and CVaR. In Chapter 3, the continuous type of CVaR model with single loss is studied. In Chapter 4, the continuous type of CVaR model with multiple losses is studied. Chapter 5 concludes the work.The main results obtained in this thesis are as follows.1. The continuous type of CVaR models with single loss is studied. The nonlinear loss functions are designed first. Based on this, a nonlinear programming model for CVaR problem is proposed, which generalized the existing linear CVaR models. Then an improved genetic algorithm is designed to solve the proposed nonlinear programming model. The simulation results indicate the proposed method can decrease the values of both CVaR and VaR.2. The continuous type of CVaR model with multiple losses is studied and a multi-objective optimization model is proposed. To overcome the limitations of traditional multi-objective optimization methods, A Pareto multi-objective genetic algorithm for multi-objective programming problems is used. The proposed model and algorithm can decrease the values of both CVaR and VaR.3. The simulations are made for the proposed algorithms by using some data on Shenzhen...