文档介绍：Portfolio Optimization with Stochastic Dominance
Constraints
Darinka Dentcheva∗ Andrzej Ruszczy´nski†
May 12, 2003
Abstract
We consider the problem of constructing a portfolio of finitely many assets whose
returns are described by a discrete joint distribution. We propose a new portfolio
optimization model involving stochastic dominance constraints on the portfolio return.
We develop optimality and duality theory for these models. We construct equivalent
optimization models with utility functions. Numerical illustration is provided.
Keywords: Portfolio optimization, stochastic dominance, risk, utility functions.
1 Introduction
The problem of optimizing a portfolio of finitely many assets is a classical problem in the-
oretical putational finance. Since the seminal work of Markowitz [19, 20, 21] it is
generally agreed that portfolio performance should be measured in two distinct dimensions:
the mean describing the expected return, and the risk which measures the uncertainty of
the return. In the mean–risk approach, we select from the universe of all possible portfolios
those that are efficient: for a given value of the mean they minimize the risk or, equivalently,
for a given value of risk they maximize the mean. This approach allows one to formulate
∗Stevens Institute of Technology, Department of Mathematics, Hoboken, NJ, e-mail:
******@stevens-
†Rutgers University, Department of Management Science and Information Systems, Piscataway, NJ 08854,
USA, e:mail: ******@
1
Portfolio Optimization with Stochastic Dominance Constraints 2
the problem as a parametric optimization problem, and it facilitates the trade-off analysis
between mean and risk.
Another theoretical approach to the portfolio selection problem is that of stochastic dom-
inance (see [23, 35, 17]). The concept of stochastic dominance is related to models of risk-
averse preferences [7]. It originated from the theory of majorization [1