Author: haroonkhan
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Do black swans exist?
The most troublesome case is when some scenarios are particularly dangerous, yet quite unlikely. How can we trust estimates of very low probabilities? To get the message, consider financial risk management. Here we need to work with extreme events (stock market crashes, defaults on sovereign debt, etc.), whose probabilities can be very low and very difficult to…
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Uncertainty about uncertainty
If we are about to launch a brand-new product, uncertainty about future sales is rather different from that in the previous case. Maybe, we know pretty well what may happen, so that the scenarios in Fig. 14.1 are known. However, it is quite hard to assess their probabilities. The following definitions, although not generally accepted, have been…
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The standard case: decision making under risk
Let us compare two random experiments: fair coin flipping and the draw of a multidimensional random variable, with a possibly complicated joint probability density. The two cases may look quite different. The first one can be represented by a quite simple Bernoulli random variable, and calculating expected values of whatever function of the outcome is…
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WHAT IS UNCERTAINTY?
When we flip a fair coin, we are uncertain about the outcome. However, we are pretty sure about the rules of the game: The coin will either land head or tail, and to all practical purposes we assume that the two outcomes are equally likely. However, what about an alien who has never seen a…
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Introduction
The presented a rather standard view of quantitative modeling. When dealing with probabilities, we have often taken for granted a frequentist perspective; our approach to statistics, especially in terms of parameter estimation, has been an orthodox one. Actually, these are not the only possible viewpoints. In fact, probability and statistics are a branch of mathematics…
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Disappointment and regret in decision making
When making decisions under risk and uncertainty in our lives, we rarely set up a utility function to formalize the problem we are facing. We come up with a solution but, unfortunately, sometimes we must admit that we were wrong. Indeed, disappointment and regret are emotions that we have all experienced. A discussion of disappointment…
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Robust optimization
Robust optimization is a label that has been attached to a fairly wide variety of optimization modeling frameworks. A rather confusing feature is that “robust” may refer to our inability to represent uncertainty reliably within a probabilistic framework; alternatively, “robust” may refer to decision-makers’ attitude towards risk taking. In this section we mainly refer to…
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ROBUSTNESS, REGRET, AND DISAPPOINTMENT
Proper scenario generation is needed to reduce sampling errors and successfully apply stochastic programming models. However, there may be more fundamental flaws in the approach: Illustrates a few issues with standard decision making procedures in a world of multiple stakeholders and subjective probabilities. In this section we just mention a couple of approaches that have…
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Scenario generation for stochastic programming
Multistage stochastic programming is a very powerful modeling framework, and it can be extended to cope with risk measures like CVaR, as we have seen in Section 13.3.3. However, the approach can be only as good as the scenario tree on which it is based. Given a multivariate probability distribution characterizing uncertainty, the most obvious way…
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Asset–liability management with transaction costs
To give the reader an idea of how to build nontrivial financial planning models, we generalize a bit the model formulation of the previous section, in order to account for proportional transaction costs. The assumptions and the limitations behind this extended model are the following: Some of the limitations of the model may easily be…