Several Portfolio Optimization Model And Algorithm

Portfolio optimization is an approach seeking equilibrium between risk and return in various financial environments. Generally, risk measures according to the recognition and reflection to markets, various frictions in pragmatic markets, and different kinds of uncertainty such as probability uncertainty and possibility uncertainty are three main aspects considered by financial analysts when they design models of portfolio optimization problems. The thesis dealt with portfolio optimization problems under fuzzy uncertainty and Knightian model uncertainty. The main innovations in the thesis are as follows.1. We propose two risk measures in possibility space, Fuzzy Value-at-Risk and Fuzzy Conditional Value-at-Risk, which are similar to those in probability space, prove that they are coherent under certain condition, and discuss their other properties. Two portfolio optimization models for fuzzy portfolio selection problems are formulated. Then a chaos genetic algorithm based on fuzzy simulation is designed. And finally computational results show that the two risk measures can play a role similar to Value-at-Risk and Conditional Value-at-Risk, and that robust solutions can be obtained when they are applied to portfolio selection problems.2. This thesis examines a new approach for credit risk measurement and portfolio optimization, based on credibility measure which has self-duality property. Fuzzy Conditional Value at Risk (FCVaR) in possibility space is produced as a credit risk measure, and a model based on the FCVaR risk measure is formulated, which can simultaneously adjust all positions in a portfolio of financial instruments in order to minimize FCVaR subject to trading and return constraints. In the approach, the credit risk possibility distributions of credit assets in considered market are described by fuzzy variables and then the optimization problem is solved effectively with a hybrid intelligent algorithm based on a fuzzy simulation method. A numerical example illustrates this approach.3. It is well known that the optimal solutions are often sensitive to perturbations in the parameters of the optimization problem. To investigate the portfolio optimization problem, we introduce uncertainty set describing the moments of returns and propose a robust approach which enables us to obtain explicit formula solutions and an efficient frontier when the estimates of parameters of uncertainty vector returns are unreliable. We believe that our approach is capable of solving the optimal portfolios for an uncertainty-averse investor who takes a conservative viewpoint.4. It is common that the information about the distribution of an uncertainty variable is exactly unknown except that its mean and covariance are known varying over an interval in practice. The optimal solutions are often sensitive to perturbations in parameters of the optimization problem model constructed from the mean and covariance. To investigate the portfolio optimization problem, this thesis proposes a robust approach maximizing worst-case utility when both the distributions underlying the uncertain vector of returns are exactly unknown and the estimates of the structure of returns are unreliable. We introduce concave convex utility function measuring the utility of investors under model uncertainty and uncertainty structure describing the moments of returns and all possible distributions and show that the robust portfolio optimization problem corresponding to the uncertainty structure can be reformulated as a parametric quadratic programming problem, enabling to obtain explicit formula solutions, an efficient frontier and equilibrium price system. This approach is an alternative of solving the optimal portfolios for an uncertainty-averse investor who takes a conservative viewpoint and identify asset mixes that have the best worst-case expected utility.5. This thesis presented multistage asset pricing principles in a no-arbitrage securities market with taxes, transaction costs and bid-ask spread, including liquidation. Some necessary and sufficient conditions are derived for the strong no-arbitrage and weak no-arbitrage. These principles can be applied in algorithm which resolves dynamic stochastic programming problem in dynamic portfolio selection.6. A multi-period mean-absolute downside deviation portfolio selection is a dynamic stochastic programming problem. In financial market with box constraints, the analytical solution of this problem is very difficult to acquire by conventional methods. We propose a hybrid intelligent method in which both a chaos genetic algorithm, based on stochastic simulation, and an artificial neural network are applied to solving the dynamic stochastic programming. The efficient frontier of the multi-period portfolio selection is obtained by this method. An illustrative case shows that the hybrid intelligent method is efficient and effective.