Robust Optimal Portfolio Based On Risk Model Of Worst

With the rapid development of global economy, the financial crisis and volatility frequently occur. Studies on wealth management and investment have been enjoying increasing theoretical and practical significance. The expected return and risk are two of the crucial factors involved in portfolio optimization. Approaches of risk measurement and the balance between assets return and assets risk are the primary problems on which investors concerned. Markowitz, an American economist, proposed the mean-variance portfolio theory in 1952, which is milestone of the modern investment theory. Along with the improvement of the modern mathematics, the studies on modern financial investment are no longer only describing or pure empirical researches, but the numerical analysis based on mathematical methods which provided deep insights in theory and efficient methods for investors.This dissertation makes a deep and systematic research on optimization and evaluation of the risk measurements based on Worst-case Lower Partial Moment (WLPM) and Worst-case Value-at-Risk. The main contributions are as follows:First, we demonstrates a risk measurement based on the worst-case lower partial moment (WLPM). WLPM is defined as a maximized lower partial of nonnegative random variable with given mean and variance. A closed-form expression of the worst-case lower partial moment in all scenarios is introduced, and then analysis of various mean-WLPM investment portfolios is shown in this dissertation. Comparisons between optimal portfolio and Markowitz model are demonstrated to assess the applicability and limitation of the mean-WLPM model.Second, this dissertation also introduces the Worst-case Value-at-Risk as the risk measurements, that is, the robust growth of optimal portfolio. Comparing to the classical optimal growth portfolio, robust growth of optimal portfolio will perform better with finite investment horizon. Furthermore, we demonstrates the process of calculation of robust optimal portfolio by re-express the worst-case value-at-risk of quadratic approximation of the growth rate in portfolio problems as a tractable positive semidefinite program. By utilizing temporal symmetry, the positive semidefinite program may be simplified as a second-order cone program which can be solved efficiently. And the optimal solution of robust optimal portfolio is obtained through the optimal solution of the second-order cone program.The dissertation apply the methods to calculate the optimal solution of robust optimal growth investment portfolio with and without risk-free assets, respectively. And we compare classical optimal growth portfolio and equal-weight portfolio by utilizing simulation and empirical data in order to assess the performance of the robust optimal portfolio.