Convex bounds for dependent risks with applications to robust optimization

Abstract

Consider a portfolio that consists of multiple assets for which the risks are dependent. Robust bounds for the risk of the portfolio given the partial dependency structure of the asset returns have received considerable attention. In this paper, we develop new convex bounds for the case with overlapping multivariate marginal dependencies. We propose an infinite dimensional linear programming based method to find these bounds in Conditional Value-at-Risk version for sum risk function and general multivariate marginal structure. Polynomial complexity results for discrete distribution case are developed for this problem. The results are extended to the approximation on the distribution of sum risk. With the tight bound on conditional value at risk of the joint portfolio, we propose a novel robust portfolio selection model that can deal with overlapping multivariate distributional information. Under some mild assumptions, the optimization problem can be solvable in polynomial time. Some numerical examples are presented.

Date of Award	3 Oct 2012
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Yan Chong CHAN (Supervisor), Simai HE (Supervisor) & Karthik Balkrishnan NATARAJAN (Supervisor)