Title: 
Robust Portfolio Selection Based on a Multi-stage Scenario Tree

Authors:
Ruijun Shen
Department of Systems Engineering and Engineering Management
The Chinese University of Hong Kong
Shatin, Hong Kong


Shuzhong Zhang
Department of Systems Engineering and Engineering Management
The Chinese University of Hong Kong
Shatin, Hong Kong

Abstract:
The aim of this paper is to apply the concept of robust
optimization introduced by Bel-Tal and Nemirovski to the portfolio
selection problems based on multi-stage scenario trees. The
objective of our portfolio selection is to maximize an expected
utility function value (or to minimize an expected disutility
function value) as in a classical stochastic programming problem,
except that we allow for uncertainties in probability
distributions along the scenario tree. We show that such a problem
can be formulated as a finite convex program in the conic form, on
which general convex optimization techniques can be applied. In
particular, if there is no short-selling, and the disutility
function takes the form of semi-variance downside risk, and all
the uncertainty sets are ellipsoidal, then the problem becomes a
second order cone programming problem and we use SeDuMi to solve
the resulting robust portfolio selection problem. Numerical
results are reported.