Decision-making under Uncertainty and Risk
|Decision Making: using in practice||4|
|The basics theory of decision-making under uncertainty||8|
|The Preference Axioms||13|
|An Introduction to Risk-Aversion||15|
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.
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.…
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