Optioned portfolio selection: Models, analysis, and solution methods

In this thesis, we mainly study the portfolio selection problem with a set of index and options of stocks, based on a refined mean-variance methodology. Models in single-stage and multistage cases are studied, with a formulation using a scenario tree structure. We first investigate the pattern of the payoff of the optimal optioned portfolio. It turns out there is a rich structure with many interesting properties, including the piecewise linearity, risk-free return at some fixed scenarios, etc. We then extend the model to accommodate the features of multistage formulations. Both the mathematical programming methodology and the stochastic control methodology are applied to solve the decision model based on a scenario tree structure. Analytical formulations of the optimal portfolio together with an expression of the efficient frontier are derived. We also make an analysis of the relations between the two approaches. We further study some variations of the mean-variance formulation. These models are applied to construct a portfolio with same preferred payoff characters, such as monotonic payoff or guaranteed payoff. Finally, the tracking model is considered in this thesis. The optimal payoff and its mean-variance efficiency are analyzed. Throughout the thesis, many numerical examples with real life data are used to illustrate and validate our results.