1 / 20

Prospect Theory: An Analysis of Decision under Risk

Prospect Theory: An Analysis of Decision under Risk . By Kahneman and Tversky , 1979, Econometrica , vol 47. Background.

danyl
Download Presentation

Prospect Theory: An Analysis of Decision under Risk

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Prospect Theory: An Analysis of Decision under Risk By Kahneman and Tversky, 1979, Econometrica, vol 47

  2. Background “Expected utility theory has generally been accepted as a normative model of rational choice and widely applied as a descriptive model of choice. It has been assumed that all reasonable people would wish to obey the axioms of the theory, and that most people actually do, most of the time.” The present paper describes several classes of choice problems in which preferences systematically violate the axioms of expected utility theory. Propose an alternative model of choice. (Prospect theory) Prospect (gamble) yields outcome xiwith probability pi (i=1, ...,n;piadd up to1) Note: The domain of the utility function (classical) includes one’s asset position (not gains and losses)

  3. Critique of the EU model – the certainty effect The certainty effect - (Allais paradox) • A= (4000,.8) vs B=(3000); 80% preferred B • C=(4000,.2) vs D=(3000,.25); 65% preferred C • The choice of B implies u(3000)/u(4000) > 4/5 • The choice of C implies the reverse inequality • Rewrite C=(4000; .20) as C=(A, .25) and rewrite D=(3000, .25) as D=(B; .25) • The substitution axiom asserts that if B preferred to A, then any probability mixture (B, p) must be preferred to (A, p) People overweight outcomes that are certain relative to outcomes which are merely probable

  4. Critique of the EU model – the reflection effect risk aversion for gains, risk proneness for losses • Consider: • A=(-4000,.8) vs B=(-3000) (92% preferred A) • C=(-4000, .2) vs D=(-3000,.25) (58% preferred D) The preference between negative prospects is the mirror image of the preference between positive prospects Note: people “hate” losses that are certain

  5. Critique of the EU model – the isolation effect People often disregard components that alternatives share. This may lead to violations of the EU model, because a pair of prospects (gambles) can be decomposed into common and distinctive components in more than one way, and different decompositions sometimes lead to different preferences. In addition to what you own, you have been given 1000. You are now asked to choose between A=(1000,.5) vs. B=(500) In addition to what you own, you have been given 2000. You are now asked to choose between C= (-1000,.5) vs. D=(-500). (majority of subjects chose B in the first choice and C in the second choice) The carriers of utility are changes of wealth, rather than final asset position

  6. Critique of the EU model Note: previous preferences conform to the reflection effect (risk aversion for positive prospects, risk seeking for negative ones) Note: when viewed in terms of final states, the two choice problems are identical (subjects did not integrate the bonus with the prospects: their reference points were different!) Insight: carriers of utility are changes of wealth (from a reference point) rather than final asset positions that include current wealth

  7. Critique of the EU model – probabilistic insurance Suppose you consider the possibility of insuring some property against damage (fire or theft). After examining the risks and the premium you find that you have no clear preference between purchasing insurance or leaving the property uninsured. A company offers a new program called probabilistic insurance. You pay half of the regular premium. In case of damage, there is a 50% chance that you pay the other half of the premium and the insurance company covers all the losses; and there is a 50% chance that you get back your payment and suffer all the losses (even vs. odd day for accident). Would you purchase probabilistic insurance? Note: represents protective action where one pays a certain cost to reduce the probability of an undesirable event --- without eliminating it altogether (burglar alarm, buying new tires)

  8. Critique of the EU model – probabilistic insurance In experiments 80% of people were against probabilistic insurance. Yet, Kahneman & Tversky (p. 270) show that expected utility theory (with a concave u) implies that probabilistic insurance is superior to regular insurance! Contingent insurance: provides the certainty of coverage against a specified type of risk (say theft), but does not cover other risks (say fire). Contingent insurance is more attractive than probabilistic insurance!

  9. Prospect Theory Two phases: (1) preliminary phase (editing) (2) phase of evaluation The editing phase consists of a preliminary analysis of the offered prospects; seeks to generate a simpler representation of these prospects. Editing consists of the application of several operations that transform the outcomes and probabilities associated with the offered prospects. In the second phase, the edited prospects are evaluated and the prospect of highest value is chosen.

  10. Operations of editing phase Coding: Coding in terms of losses and gains from a reference point (usually the current asset position)  Combination of probabilities with identical outcomes  Segregation: if possible, segregate the riskless component from the risky one. For example (300,.8; 200,.2) is naturally decomposed into a sure gain of 200 and the risky prospect (100,.8)  Cancellation: discarding of components shared by the offered prospects (isolation effect)  Simplification: rounding, discarding of extremely unlikely outcomes Detection of dominance: rejection of dominated alternatives

  11. Editing phase In the coding phase, what reference point should be used? • Formation of reference point • Can the reference point change over time? Do we understand how? Note: Many anomalies of preference result from the editing of prospects. The final edited prospects may depend on the order of performing these operations. A descriptive, not a prescriptive theory of choice.

  12. Evaluation phase The overall value V of an edited prospect is expressed in terms of two scales, Πand v. Π associates with each probability p a weight Π(p), which reflects the impact of p on the over-all value of the prospect. The second scale, v assigns to each outcome x a number v(x), which reflects the subjective value of that outcome. Note 1: Π is not a probability measure Note 2: Outcomes are defined relative to a reference point (the zero point of the value scale). v measures the value of deviations from the reference point, i.e. gains and losses.

  13. Evaluation phase Consider simple prospects of the form (x,p;y,q). A prospect is regular, if it is neither strictly positive nor strictly negative. Otherwise it is not regular. If (x,p;y,q) is a regular prospect, then V(x,p;y,q)= Π(p)v(x) + Π(q)v(y), where v(0)=0, (0)=0, and (1)=1 For example: V(400,.25; -100,.75) = Π(.25)v(400) + Π(.75)v(-100)

  14. Evaluation phase The evaluation of strictly positive and strictly negative prospects follows a different rule. In the editing phase such prospects are segregated into two components: the riskless component and the risky component (the actual additional gain or loss which is at stake) If (x,p;y,q) is not a regular prospect, i.e. is either strictly positive or negative, and x is the more extreme outcome V(x,p;y,q) = v(y) + Π(p)[v(x)-v(y)] For example V(400,.25; 100,.75) = v(100) + (.25)[v(400)-v(100)]

  15. The value function (1) Value function defined on deviations from the reference point (changes in assets or wealth) (2) It is generally concave above the reference point (gains), convex below the reference point (losses). (3) Value function steeper for losses than for gains.

  16. The value function

  17. The weight function General principle: The value of each outcome is multiplied by a decision weight. Decision weights are not probabilities! They do not have to obey the probability axioms. Decision weights measure the impact of events on the desirability of prospects, and not merely the perceived likelihood of these events. We express decision weights as a function of the probabilities, although other factors could influence them as well.

  18. The weight function

  19. Properties of the weight function Π is an increasing function of p Π(0)=0, Π(1)=1(scaling) For small p: Π(p) > p (small probabilities are overweighted) (may contribute to the attractiveness of gambling and insurance) Decision weights are generally smaller than the corresponding probabilities, except for small p Generally Π(p) + Π(1-p) < 1 (subcertainty) Subproportionality: Π(pq)/ Π(p) ≤ Π(pqr)/ Π(pr) (log(Π) is a convex function of log p) Note: dominated alternatives are assumed to have been detected and eliminated

  20. Conclusions Prospect theory can account for many observed ”anomalies” of decision behavior: • via changing reference point (A house, B house) • via form of the value functions (concave for gains, convex for losses – steeper for losses) • via overweighting small probabilities

More Related