Data-driven Multistage Distributionally Robust Optimization with Nested Distance: Time Consistency and Tractable Dynamic Reformulations

We study multistage distributionally robust optimization in which the uncertainty set consists of stochastic processes that are close to a scenario tree in the nested distance (Pflug and Pichler (2012)). Compared to other choices such as Wasserstein distance between stochastic processes, the nested distance accounts for information evolution, making it hedge against a plausible family … Read more

Assessing the Cost of the Hazard-Decision Simplification in Multistage Stochastic Hydrothermal Scheduling

Hydropower is one of the world’s primary renewable energy sources whose usage has profound economic, environmental, and social impacts. We focus on the dispatch of generating units and the storage policy of hydro resources. In this context, an accurate assessment of the water opportunity-cost is cru- cial for driving the sustainable use of this scarce … Read more

Risk averse stochastic programming: time consistency and optimal stopping

Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic optimization. The problem is stated in generality first. The paper discusses time consistent decision-making by addressing risk measures which are recursive, nested, dynamically … 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

Time inconsistency of optimal policies of distributionally robust inventory models

In this paper, we investigate optimal policies of distributionally robust (risk averse) inventory models. We demonstrate that if the respective risk measures are not strictly monotone, then there may exist infinitely many optimal policies which are not base-stock and not time consistent. This is in a sharp contrast with the risk neutral formulation of the … Read more

Interchangeability principle and dynamic equations in risk averse stochastic programming

In this paper we consider interchangeability of the minimization operator with monotone risk functionals. In particular we discuss the role of strict monotonicity of the risk functionals. We also discuss implications to solutions of dynamic programming equations of risk averse multistage stochastic programming problems. Article Download View Interchangeability principle and dynamic equations in risk averse … Read more

Time and Dynamic Consistency of Risk Averse Stochastic Programs

In various settings time consistency in dynamic programming has been addressed by many authors going all the way back to original developments by Richard Bellman. The basic idea of the involved dynamic principle is that a policy designed at the first stage, before observing realizations of the random data, should not be changed at the … Read more

Decomposability and time consistency of risk averse multistage programs

Two approaches to time consistency of risk averse multistage stochastic problems were dis- cussed in the recent literature. In one approach certain properties of the corresponding risk measure are postulated which imply its decomposability. The other approach deals directly with conditional optimality of solutions of the considered problem. The aim of this paper is to … Read more

Rectangular sets of probability measures

In this paper we consider the notion of rectangularity of a set of probability measures, introduced in Epstein and Schneider (2003), from a somewhat different point of view. We define rectangularity as a property of dynamic decomposition of a distributionally robust stochastic optimization problem and show how it relates to the modern theory of coherent … Read more

Time (in)consistency of multistage distributionally robust inventory models with moment constraints

Recently, there has been a growing interest in developing inventory control policies which are robust to model misspecification. One approach is to posit that nature selects a worst-case distribution for any relevant stochastic primitives from some pre-specified family. Several communities have observed that a subtle phenomena known as time inconsistency can arise in this framework. … Read more