Optimization of Convex Risk Functions

Authors:
Andrzej Ruszczyński;Alexander Shapiro
Affiliations:
Department of Management Science and Information Systems, Rutgers University, Piscataway, New Jersey 08854;School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Venue:
Mathematics of Operations Research
Year:
2006

Citing 2
Cited 22

Duality in stochastic linear and dynamic programming

Duality in stochastic linear and dynamic programming
Dual Stochastic Dominance and Related Mean-Risk Models

SIAM Journal on Optimization

Conditional Risk Mappings

Mathematics of Operations Research
Simulating Sensitivities of Conditional Value at Risk

Management Science
Goal-Driven Optimization

Operations Research
Constructing Risk Measures from Uncertainty Sets

Operations Research
A multiobjective metaheuristic for a mean-risk multistage capacity investment problem

Journal of Heuristics
Minimizing measures of risk by saddle point conditions

Journal of Computational and Applied Mathematics
A multiobjective metaheuristic for a mean-risk static stochastic knapsack problem

Computational Optimization and Applications
A Soft Robust Model for Optimization Under Ambiguity

Operations Research
Risk-Averse Two-Stage Stochastic Linear Programming: Modeling and Decomposition

Operations Research
A Multiproduct Risk-Averse Newsvendor with Law-Invariant Coherent Measures of Risk

Operations Research
Selecting Optimal Alternatives and Risk Reduction Strategies in Decision Trees

Operations Research
Optimizing the Societal Benefits of the Annual Influenza Vaccine: A Stochastic Programming Approach

Operations Research
Risk Averse Shape Optimization

SIAM Journal on Control and Optimization
Generation Capacity Expansion in a Risky Environment: A Stochastic Equilibrium Analysis

Operations Research
A dynamic programming approach to adjustable robust optimization

Operations Research Letters
A risk-averse newsvendor with law invariant coherent measures of risk

Operations Research Letters
On a time consistency concept in risk averse multistage stochastic programming

Operations Research Letters
Optimization Under Probabilistic Envelope Constraints

Operations Research
Risk Preferences and Their Robust Representation

Mathematics of Operations Research
On Kusuoka Representation of Law Invariant Risk Measures

Mathematics of Operations Research
Entropy Coherent and Entropy Convex Measures of Risk

Mathematics of Operations Research
SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of measurable functions, we develop new representation theorems for risk models, and optimality and duality theory for problems with convex risk functions.