Chapter 10: Risk Aversion Flashcards
Unsurprisingly, many of the decision made by Decision Makers are made with the goal of being _____________ _______________.
risk averse.
Types of Risk Aversion (3)
1) Actuarial Risk Aversion
2) Aversion Against Utility Risks
3) Epistemic Risk Aversion
Actuarial Risk Aversion
(Review Golf Ball Example in Notes)
A decision maker is risk averted if one, starts with certainty, is unwilling to bet in an actuarilly fair gamble.
_____________ ____________ _______________ is consistent with _______________ ____________ ______________, and can be _____________ on a ______________.
Actuarial Risk Aversion; Maximizing Expected Utility; plotted; graph
If the Decision maker’s __________ function for an object ($1M, apple, etc.) is “____________,” on a graph, then the more ___________ ______________ the decision maker is: the expected _______________ of a _____________ prize (___) is greater than the ____________ of ______________ (___ ___) and _____________ prizes (___).
(Review Apple Gamble Example in Notes)
utility; concave; risk averse; utility; small; (n); utility; larger; (2n); smaller; (n)
Dotted Linear Line on Graph means…
(Review Apple Gamble Example in Notes)
Represents someone who is actuarilly risk neutral: the expected utility of 2n and 0 are the same.
Solid “Concave” Line on Graph means…
(Review Apple Gamble Example in Notes)
Represents someone who is actuarilly risk averse: utility of n is greater than 2n and 0.
Aversion to Utility Risks (Rabin Explanation)
- It’s a Maximizing Expected Utility Orthodoxy (doesn’t use / inconsistent with MEU)
- Takes issue with Allais Paradox because the requirements imposed by the Allais Paradox are preposterous.
- Ex. You decline a gamble wherein winning will earn you $110 and losing will cost you $100. Following from the MEU framework, this means you would also necessarily have to decline a gamble wherein losing cost you $600, and where you could win whatever amount of money whatsoever.
- A step further, let’s say you decline a gamble between winning $125, and losing $110. According to the MEU framework, there’s NO amount of money WHATSOEVER that could be offered to you, in winning, in a gamble in which you lose $1,000.
- These obligations are ludicrous. An agent’s marginal utility for money deteriorates far too fast, caused ABSURD RISK AVERSION. it cost the agent potentially lucrative gambles, that would be rationally permissible to accept.
- These obligations, based on an agent’s preferences for their current level of wealth over a gamble between some amount of money above and below their current level of wealth, holds as long as one’s utility function is concave.
Aversion to Utility Risk (Rabin Theorem)
u (W + z) = (10/11)ʸ * u(x) ; where y = 1 + ((z - 11)/21)
W: Current level of wealth
z: value above your current level of wealth (addition above current level of wealth)
10: potential loss
11: potential gain
y: Number of Dollar Windows
u(x): Utility of W - potential loss (10)
21: potential loss (10) + potential gain (11)
Risk Aversion does have an ________________ component, and is ________________ with the principle of _________________ _________________ ___________________, and therefore also inconsistent with _________________ risk aversion.
Epistemic; inconsistent; maximizing expected utility; Actuarial
Explain the Tennis Match
(Cross-references notes as needed)
You attend a set of 3 Tennis Matches: A, B, C
Match A:
- You know each player very well. Based ont their respective skill sets, you believe they’re evenly matched, and hence assign a 50/50 chance to each player for winning
- You honestly believe each player has an equal probability of winning.
- Here, your assignment of probability assessments is epistemically robust.
Match B:
- You don’t know either of the players very well, or their skill sets.
- So you have no choice but to be an equal opportunist, and assign each player a probability of 50/50 of winning the match.
- Here, your assignment of probability assessements are NOT epistemically robust.
Match C:
- Similarly to Match B, you don’t really know each player at all / skill sets.
- All you know is that these players aren’t evenly matched; one player is far better than another, HOWEVER, you don’t know who this player is among the two.
- So, you have no choice but to assign a 50/50 probability to each of the player’s winning here as well.
You are now offered to place bets on each event. You will either win or lose $100 each match depending on who wins the match.
Gardenfors and Salhin, the Philosophers who constructed this tennis match problem state that…
1) If one’s willing to place a bet of _________ odds in the ____st Match (__), then they should necessarily be willing to place equal odds for the other _______ matches (__ and __).
2) HOWEVER, it’s rational that one would only place a _______ on the ________ Match and not the others, GIVEN that they have _____________ KNOWN probabilities for the _____st Match only.
equal; 1st; A; two; B; C
bets; 1st; RELIABLE; 1st
This Tennis Match Problem is meant to demonstrate how one is more comfortable with making decisions based on ______________ probabilities, and are _____________ more preferrable than making decisions based on ______________ probabilities.
known; ALWAYS; unknown
How would you assign probability functions to Match C ?
(Refer to notes as needed)
- Keep in mind, you don’t really know anything about the players, other than that one of the players is much better than the other.
So, the best we can do is assign TWO separate probability functions: where one of the players has a higher probability of winning and the other is not, then vice versa.
Probability Function 1) Player One = 0.9, Player Two = 0.1
Probability Function 2) Player One = 0.1, Player Two = 0.9
How would you assign proability functions in Match B?
(Refer to notes as needed)
- Well here we don’t know anything about our respective players in this match.
- We don’t know any of the probability functions that could be applied to either of the players [that make up 1.0], so we would have to assign several probability functions to each player’s winning the game.
- …Such that the number of subjective probabilities we’d have to assign to each player winning the game is infinite.