Markowitz's model with intractable liabilities

Abstract

This thesis studies robust Markowitz's models with unhedgeable liabilities involved in the final decision. The term "unhedgeable liabilities" refers to the liabilities about which the only things we know are their distributions or a few moments. With the robust idea, the target of the investor is set to minimize the variance of her portfolio in the worst scenario over all possible unhedgeable liabilities that could happen. Because of the time-inconsistent nature of the problem, the classical dynamic programming and stochastic control approaches cannot be directly applied to solve it. Instead, the quantile optimization method is adopted to tackle the problem. Using relaxation method, the optimal solutions to this specific kind of problem are derived in closed-form, and the properties of the mean-variance frontier are fully discussed too. As we know, this thesis is the first to introduce unhedgeable liabilities into mean-variance formulation, which further generalizes the original mean-variance field and also to some extent draws the model to the real .nancial world. Since the components of the terminal wealth in our model are based on different markets, a new risk measure is also put forward to avoid the ill-posedness of the problem.