choice under risk/ uncertainty

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Last updated 6:17 PM on 4/26/26
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19 Terms

1
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risk

  • probabilities are known

  • e.g. coint toss: P(heads) = 0.5

2
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uncertainty

  • probabilities are unknown/ subjecive

3
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excpected value

  • average monetary payoff

  • pi= probability

  • xi= payoff

<ul><li><p>average monetary payoff </p></li><li><p>pi= probability</p></li><li><p>xi= payoff</p></li></ul><p></p>
4
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st petersburg paradox

lottery:

  • first heads = £2

  • second heads =£4

  • third head = £8

  • etc

  • excpected value - see image

  • but people will not pay infinite money to play

  • this meas ev alone cannot explain behaviour

<p>lottery:</p><ul><li><p>first heads = £2</p></li><li><p>second heads =£4</p></li><li><p>third head = £8</p></li><li><p>etc</p></li><li><p>excpected value - see image</p></li><li><p>but people will not pay infinite money to play</p></li><li><p>this meas ev alone cannot explain behaviour</p></li></ul><p></p>
5
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excpected utility theory

  • people maxamise utility not money

  • u(x)= utility from money x

<ul><li><p>people maxamise utility not money</p></li><li><p>u(x)= utility from money x</p></li><li><p></p></li></ul><p></p>
6
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marginal utility

  • extra utility from one more unit

  • more money increases utility

<ul><li><p>extra utility from one more unit</p></li><li><p>more money increases utility</p></li><li><p></p></li></ul><p></p>
7
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diminishing marginal utility

  • each extra unit gives less happiness

  • thus risk aversion

<ul><li><p>each extra unit gives less happiness</p></li><li><p>thus risk aversion</p></li><li><p></p></li></ul><p></p>
8
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risk avesion condition

  • concave utility

  • u”(X)<0

9
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certainty equivilent

  • guaranteed amount giving same utility as lottery

<ul><li><p>guaranteed amount giving same utility as lottery</p></li></ul><p></p>
10
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risk premium

  • amount willing to pay to avoid risk

  • RP = EV-CE

11
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risk loving

  • prefers gamble over EV

  • convex utility

  • u”(X)>0

12
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risk neutral

  • linear utility

  • u”(X)= 0

13
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independence axiom

  • if p>q then mixing both with same third party preserves ranking

  • very important!!!

<ul><li><p>if p&gt;q then mixing both with same third party preserves ranking</p></li><li><p>very important!!!</p></li></ul><p></p>
14
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archmedean axiom

  • no lottery infinitely better than another

15
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ambiguity

  • situations where probability of outcome is unkown or subjective

16
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subjective excpected utility

a theory where decision makers form their own subjective excpectations of probabilities and choose the act with the highest utility

17
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calculating utility of an act

f = act

<p>f = act</p>
18
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act

  • an action defined by the specifc outcome it provdies in each possible state of the world

19
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states of the world

  • an exclusive and exhastive list of all possible outcomes in a given scenario