ajaz_204_2009_lecture_21

ajaz_204_2009_lecture_21 - University of Toronto Department...

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University of Toronto Department of Economics ECO 204 2009 2010 Sayed Ajaz Hussain Lecture 21 1 Ajaz Hussain. Department of Economics. University of Toronto (St. George)
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Today ± Probability: 3 interpretations and rules ± Decision making under uncertainty: expected utility (EU) criterion ± Attitude towards risk and utility functions ± Risk Neutral decision maker: use either EV or EU ± Is crime “rational”? ± Attitudes towards Risk: Definitions ± Certainty Equivalence ± Deriving utility function Ajaz Hussain. Department of Economics. University of Toronto (St. George) 2
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Further Readings Fooled by Randomness Black Swan Against the Gods Real Options Ajaz Hussain. Department of Economics. University of Toronto (St. George) 3
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Decision Making Under Uncertainty We (mostly) consider models with: Discrete Choices & Pecuniary Outcomes Examples: {Invest, Don’t Invest} {Invest Today, Invest Tomorrow, Don’t Invest} Ajaz Hussain. Department of Economics. University of Toronto (St. George) 4
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Example: Investment Under Uncertainty Ajaz Hussain. Department of Economics. University of Toronto (St. George) 5 Decision? Invest Chance Success: $800 $200 = $600 Failure: $200 Don’t Invest $0 P(S) = 0.6 P(F) = 0.4
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Probability: 3 Interpretations Objective/Natural Examples: Coin, Die Frequency Examples: Accident rates, Disease, Life expectancy Subjective/Bayesian Examples: Ajaz Hussain. Department of Economics. University of Toronto (St. George) 6
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Probability “Rules” Regardless of probability interpretation, the rules of probabilities are the same. Probability of an event is between 0 and 1 Suppose the event is A. Then: 0 P(A) 1 Probability of all events = 1 Ajaz Hussain. Department of Economics. University of Toronto (St. George) 7
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Example: Coin Toss and Die Roll Ajaz Hussain. Department of Economics. University of Toronto (St. George) 8 123456 Heads Tails Probability of observing all 12 outcomes: P(all outcomes) = 12/12 = 1 Probability of observing (say) Heads: P(H) = 6/12 = ½ Probability of observing Heads and 4: P(H4) = 1/12
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Conditional Probability Probability of event A given that event B occurred: P(A|B) = P(AB)/P(B) Ajaz Hussain. Department of Economics. University of Toronto (St. George) 9 123456 Heads Tails Probability of H given that 4 has been observed P(H|4) = P(H4)/P(4) = (1/12)/(2/12) = ½
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Independent Events If two events A and B are independent then: P(A|B) = P(A) Event B gives no additional information about Event A P(A|B) = P(AB)/P(B) = P(A) This is true only if P(AB) = P(A)P(B) P(A|B) = P(AB) /P(B) = P(A)P(B) /P(B) = P(A) Ajaz Hussain. Department of Economics. University of Toronto (St. George) 10
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Independent Events Events A and B are independent if: P(A|B) = P(A) Ajaz Hussain. Department of Economics. University of Toronto (St. George) 11 123456 Heads Tails P(H|4) = P(H4) / P(4) = (1/12) / (2/12) = ½ P(H|4) = P(H) P(H4) = P(H)P(4) = (6/12) (2/12) = 1/12
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Example: Investment Under Uncertainty Ajaz Hussain. Department of Economics.
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ajaz_204_2009_lecture_21 - University of Toronto Department...

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