Category: Decision Making Under Risk

So far, in terms of concrete procedures, we have considered only decision trees, which are well suited to cope with discrete decisions, when uncertainty can be represented by a finite set of scenarios. More generally, we would like to solve a problem like where S is a subset of , and the expectation can be taken with respect… Continue reading TWO-STAGE STOCHASTIC PROGRAMMING MODELS

Given the limitations of standard deviation and variance as risk measures, alternative ones have been proposed. To be specific, we will refer once more to a financial investment problem, where risk is related to portfolio loss. The most widely known such measure is value at risk [VaR; not to be confused with variance (Var)]. The VaR concept… Continue reading Quantile-based risk measures: value at risk

If asked about our utility function, we would hardly be able to give a sensible answer. However, in real life, we do trade off expectations against risk; to do so, we need a way to measure risk. DEFINITION 13.1 A risk measure is a function ρ(X), mapping a random variable X into the set of nonnegative real numbers . In… Continue reading Mean–risk optimization

So far, when dealing with a decision problem under risk, we have used expected profit or expected cost as the criterion of choice. We did so, e.g., for the newsvendor problem,2 as well as for the decision trees of the previous section. But does this actually make sense? The following examples show that this need not… Continue reading RISK AVERSION AND RISK MEASURES

Decision trees are a very simple tool for framing decision problems with a discrete set of alternatives and a discrete representation of uncertainty. We may start moving to more complicated cases by expressing a decision problem under risk in a more general way: It is important to understand what problem (13.1) represents: This is a here-and-now decision,… Continue reading Expected value of perfect information

Decision trees are a natural way to describe decision problems under risk, involving a sequence of decisions among a finite set of alternative options and a set of discrete scenarios, modeling uncertain outcomes that follow our decisions. Actually, we have already dealt with decision trees informally in earlier examples.1 Now we should treat this formalism more… Continue reading DECISION TREES

This represents a synthesis of what we have become acquainted with so far. Decision making under uncertainty is a quite challenging topic, merging probability theory and statistics with optimization modeling. This mix may result in quite demanding mathematics, which we will avoid by focusing on fundamental concepts and a few illustrative toy examples to clarify… Continue reading Introduction