## Bilevel optimization with a multi-objective lower-level problem: Risk-neutral and risk-averse formulations

In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the deterministic case and have never been studied from a stochastic approximation viewpoint despite the recent advances in stochastic methods for single-level, bilevel, and multi-objective … Read more

## Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming

In this tutorial we discuss several aspects of modeling and solving multistage stochastic programming problems. In particular we discuss distributionally robust and risk averse approaches to multistage stochastic programming, and the involved concept of time consistency. This tutorial is aimed at presenting a certain point of view of multistage stochastic programming, and can be viewed … Read more

## Data-Driven Risk-Averse Two-Stage Stochastic Program with ζ-Structure Probability Metrics

The traditional two-stage stochastic programming approach assumes the distribution of the random parameter in a problem is known. In most practices, however, the distribution is actually unknown. Instead, only a series of historic data are available. In this paper, we develop a data-driven stochastic optimization approach to providing a risk-averse decision making under uncertainty. In … Read more

## A distribution-free risk-reward newsvendor model: Extending Scarf’s min-max order formula

Scarf’s min-max order formula for the distribution-free risk-neutral newsvendor problem is a classical result in the field of inventory management. The min-max order formula provides, in closed-form, the order quantity that maximizes the worst-case expected profit associated with the demand of a single product when only the mean and variance of the product’s demand distribution, … Read more

## Risk neutral and risk averse Stochastic Dual Dynamic Programming method

In this paper we discuss risk neutral and risk averse approaches to multistage (linear) stochastic programming problems based on the Stochastic Dual Dynamic Programming (SDDP) method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system. Citation Article Download View Risk neutral and risk … Read more

## A Multi-Product Risk-Averse Newsvendor with Law Invariant Coherent Measures of Risk

We consider a multi-product newsvendor under the law-invariant coherent risk measures. We first establish a few fundamental properties of the model regarding the convexity of the problem, the symmetry of the solution and the impact of risk aversion. Specifically, we show that for identical products with independent demands, increased risk aversion leads to decreased orders. … Read more