Results 1 
5 of
5
Theory and applications of Robust Optimization
, 2007
"... In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most pr ..."
Abstract

Cited by 110 (16 self)
 Add to MetaCart
(Show Context)
In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most prominent theoretical results of RO over the past decade, we will also present some recent results linking RO to adaptable models for multistage decisionmaking problems. Finally, we will highlight successful applications of RO across a wide spectrum of domains, including, but not limited to, finance, statistics, learning, and engineering.
Large Scale Portfolio Optimization with Piecewise Linear Transaction Costs
, 2008
"... We consider the fundamental problem of computing an optimal portfolio based on a quadratic meanvariance model for the objective function and a given polyhedral representation of the constraints. The main departure from the classical quadratic programming formulation is the inclusion in the objecti ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
We consider the fundamental problem of computing an optimal portfolio based on a quadratic meanvariance model for the objective function and a given polyhedral representation of the constraints. The main departure from the classical quadratic programming formulation is the inclusion in the objective function of piecewise linear, separable functions representing the transaction costs. We handle the nonsmoothness in the objective function by using spline approximations. The problem is first solved approximately using a primaldual interiorpoint method applied to the smoothed problem. Then, we crossover to an active set method applied to the original nonsmooth problem to attain a high accuracy solution. Our numerical tests show that we can solve large scale problems efficiently and accurately.
Robust portfolio selection based on a joint ellipsoidal uncertainty set
 Optimization Methods & Software
, 2011
"... The “separable ” uncertainty sets have been widely used in robust portfolio selection models (e.g., see [16, 15, 28]). For these uncertainty sets, each type of uncertain parameters (e.g., mean and covariance) has its own uncertainty set. As addressed in [21, 22], these “separable ” uncertainty sets ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
The “separable ” uncertainty sets have been widely used in robust portfolio selection models (e.g., see [16, 15, 28]). For these uncertainty sets, each type of uncertain parameters (e.g., mean and covariance) has its own uncertainty set. As addressed in [21, 22], these “separable ” uncertainty sets typically share two common properties: (i) their actual confidence level, namely, the probability of uncertain parameters falling within the uncertainty set is unknown, and it can be much higher than the desired one; and (ii) they are fully or partially boxtype. The associated consequences are that the resulting robust portfolios can be too conservative, and moreover, they are usually highly nondiversified as observed in the computational experiments conducted in [21, 22] and [28]. To combat these drawbacks, we consider a factor model for the random asset returns. For this model, we introduce a “joint ” ellipsoidal uncertainty set for the model parameters and show that it can be constructed as a confidence region associated with a statistical procedure applied to estimate the model parameters. We further show that the robust maximum riskadjusted return (RMRAR) problem with this uncertainty set can be reformulated and solved as a cone programming problem. The computational results reported in [21, 22] demonstrate that the robust portfolio determined by the RMRAR model with our “joint ” uncertainty set outperforms that with Goldfarb and Iyengar’s “separable ” uncertainty set proposed in the seminal paper [16] in terms of wealth growth rate and transaction cost; and moreover, our robust portfolio is fairly diversified, but Goldfarb and Iyengar’s is surprisingly highly nondiversified. Key words: Robust optimization, meanvariance portfolio selection, maximum riskadjusted return portfolio selection, cone programming, linear regression.
Strong formulations of robust . . .
, 2006
"... We introduce strong formulations for robust mixed 0–1 programming with uncertain objective coefficients. We focus on a polytopic uncertainty set described by a “budget constraint” for allowed uncertainty in the objective coefficients. We show that for a robust 0–1 problem, there is an α–tight linear ..."
Abstract
 Add to MetaCart
We introduce strong formulations for robust mixed 0–1 programming with uncertain objective coefficients. We focus on a polytopic uncertainty set described by a “budget constraint” for allowed uncertainty in the objective coefficients. We show that for a robust 0–1 problem, there is an α–tight linear programming formulation with size polynomial in the size of an α–tight linear programming formulation for the nominal 0–1 problem. We give extensions to robust mixed 0–1 programming and present computational experiments with the proposed formulations.
A Robust Optimization Approach For Static Portfolio Management
, 2008
"... A robust optimization approach for static portfolio ..."