Risk management

Abstract

In Chapter 2 we study the basic formulation of decision-making problems using stochastic programming. In these problems we consider that the objective of the decision-making agents is either maximizing profit (e.g., the financial profit of an electricity producer) or minimizing cost (e.g., the electricity procurement cost of an industrial consumer). In stochastic programming, where uncertain data are modeled as stochastic processes, the profit or cost is a random variable that can be characterized by a probability distribution. In an optimization problem involving a random objective function it is necessary to optimize a function characterizing the distribution of this random variable, for instance, its expected value. This is the criterion that is generally used in stochastic programming problems. Therefore, the problem consisting in maximizing “the profit” obtained by a decision-making agent results in maximizing the expected profit achieved by this agent.