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Decision-making under Uncertainty and Risk
Nr. | Название главы | Стр. |
Introduction | 3 | |
Decision Making: using in practice | 4 | |
Decision trees | 5 | |
The basics theory of decision-making under uncertainty | 8 | |
Expected Value | 9 | |
Quiz | 10 | |
The Preference Axioms | 13 | |
An Introduction to Risk-Aversion | 15 | |
Conclusion | 20 | |
References | 21 |
The term "expected value" provides one possible answer to the question: How much is
a gamble, or any risky decision, worth? It is simply the sum of all the possible outcomes of
a gamble, multiplied by their respective probabilities.
To illustrate:
1. Say you're feeling lucky one day, so you join your office betting pool as they follow the Kentucky Derby and place $10 on Santa's Little Helper, at 25/1 odds. You know that in the unlikely event of Santa's Little Helper winning the race, you'll be richer by 10 * 25 = $250.
What this means is that, according to the bookmaker of the betting pool, Santa's Little Helper has a one in 25 chance of winning and a 24 in 25 chance of losing, or, to phrase it mathematically, the probability that Santa's Little Helper will win the race is 1/25.
So what's the expected value of your bet? Well, there are two possible outcomes - either Santa's Little Helper wins the race or he doesn't. If he wins, you get $250; otherwise, you get nothing. So the expected value of the gamble is:
(250 * 1/25) + (0 * 24/25) = 10 + 0 = $10
And $10 is exactly what you would pay to participate in the gamble.
2. Another example:
A pharmaceutical company faced with the opportunity to buy a patent on a new technology for $200 million, might know that there would be a 20% chance that it would enable them to develop a life-saving drug that might earn them, say $500 million; a 40% chance that they might earn $200 million from it; and a 40% chance
that it would turn out worthless.
The expected value of this patent would then be:
(500,000,000 * 0.2) + (200,000,000 * 0.4) + (0 * 0.4) = $180 million.…
Virtually all decisions are made in an environment to at least some uncertainty. However, the degree will vary from relative certainty to great uncertainty. There are certain risks involved in making decisions. In a situation involving certainty, people are reasonably sure about what will happen when they make a decision. The information is available and is considered to the reliable, and the cause and effect relationship are known. In situation of uncertainty, on the other hand, people have only a meager database, they do not know whether or not the data are reliable, and they are very unsure about whether or not the situation may change. Moreover, they cannot evaluate the interactions of the different variables. For example, a corporation that decides to expand its Operation to an unfamiliar country may know little about the country’s culture, laws, economic environment, and politics. The political situation may be volatile that even experts cannot predict a possible change in government. In situation with risks, factual information may exist, but it may be incomplete. To improve decision making one may estimate the objective probability of an outcome by using, for example, mathematical models on the other hand, subjective probability, based on judgment and experience may be used. All intelligent decision makers dealing with uncertainty like to know the degree and nature of the risk they are taking in choosing a course of action. One of the deficiencies in using the traditional approaches of operations research for problem solving is that many of the data used in model are merely estimates and others are based on probabilities. The ordinary practice is to have staff specialists coming up with “best estimates”.
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