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![Evaluation Phase
• Prospect theory distinguishes between evaluation of strictly positive/negative
and regular prospects.
• A regular prospect is defined as p + q < 1 or x ≥ 0 ≥ y or x ≤ 0 ≤ y; and the
corresponding evaluation is V(x, p; y, q) = ∏(p)v(x) + ∏(q)v(y).
• A strictly positive/negative prospect is defined as p + q = 1 and either x > y > 0 or
x < y < 0; and the corresponding evaluation is v(y) + ∏(p)[ v(x) - v(y) ].
• if ∏ (p) + ∏ (l - p) = 1 both evaluation are the same.
• What are the properties of v(.) and ∏(.)?](https://image.slidesharecdn.com/prospecttheory-160515154150/85/Prospect-theory-14-320.jpg)
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Prospect theory
- 1. Prospect Theory Amir MohammadTahamtan
- 2. Outline • Expected UtilityTheory • Phenomena Violating EXU Theory • Solving the inconsistencies • Theory of Prospect Theory • Some Evidence That support Prospect Theory
- 3. The EXU Theory •Expectation: U(X,P) = u(X)∙P, where X is the vector of the outcomes and P is the corresponding probabilities • Acceptable asset position: U(X + w, p) > u(w) = U(w); the domain of the utility function is final states rather than gains or losses • Risk aversion: u is concave, u”< 0
- 4. Phenomena Violating TheEXU Theory • Violation of the substitution/independence axiom • The isolation effect: discarding components that are shared by all prospects. • Framing effects • Nonlinear preferences: nonlinearity of preferences in probability • Source dependence • Risk seeking: a gain with small probability but a loss with large probability • Loss aversion: losses loom larger than gains
- 5. Violation of substitutionaxiom: the certainty effect
- 6. Violation of substitutionaxiom: another type
- 7.
- 8. A schematic viewof the problem 10
- 9.
- 10. Does varying theoutcomes of a prospect have an impact on preference as well?
- 11. How to solvethese inconsistencies • Assigning value to gains and losses rather than to final assets • Replacing probabilities by decision weights
- 12. Prospect Theory A choiceis made in a two phase process: • Editing phase: a preliminary analysis of the offered prospects yielding a simpler representation of these prospects. • Evaluation phase: the prospect of highest value is chosen.
- 13. Editing phase • Coding:viewing the prospect as gain or loss • Combination: simplifying the prospect by combining the probabilities associated with identical outcomes • Segregation: segregating risky and riskless components of the prospect • Cancellation: the discarding of common constituents, i.e., outcome-probability pairs. • Simplification: rounding probabilities and outcomes. (101, .49) (100,.50) • Dominance: the scanning of offered prospects to detect dominated alternatives
- 14. Evaluation Phase • Prospecttheory distinguishes between evaluation of strictly positive/negative and regular prospects. • A regular prospect is defined as p + q < 1 or x ≥ 0 ≥ y or x ≤ 0 ≤ y; and the corresponding evaluation is V(x, p; y, q) = ∏(p)v(x) + ∏(q)v(y). • A strictly positive/negative prospect is defined as p + q = 1 and either x > y > 0 or x < y < 0; and the corresponding evaluation is v(y) + ∏(p)[ v(x) - v(y) ]. • if ∏ (p) + ∏ (l - p) = 1 both evaluation are the same. • What are the properties of v(.) and ∏(.)?
- 15. The value functionv(.) • The carriers of value are changes in wealth or welfare, rather than final states. • v(.) is concave for gains and convex for losses • v(-y) – v(-x) > v(x) –v(y): loss looms larger!
- 16. Evidence for concavityof v(.)
- 17. The weighting function∏(.) • ∏ is an increasing of p, with ∏ (0) = 0 and ∏ (1) = 1. • For small values of p, ∏ is a sub-additive function of p, i.e., ∏ (r.p)> r∏ (p) for 0< r < 1. • For small p, ∏ (p) > p; small probabilities are overweighted. • There is evidence that for all 0 < p <1, ∏ (p) + ∏ (1 - p) < 1.
- 18. Evidence for overweightingsmall probability ∏ (.001)v(5,000)>v(5)∏ (.001)>v(5)/v(5,000)>.001
Editor's Notes
- #6 If lottery L is preferred to lottery L’, then any linear combination of L is also preferred to L’.
- #8 78% chose 3000. Problem 10 and 4 are identical in terms of final outcomes and probabilities.
- #10 Implications of the table: the reflection effect implies that risk aversion in the positive domain is accompanied by risk seeking in the negative domain. preferences both in the positive and negative frame are in contrast with the EXU theory. the reflection effect eliminates aversion for uncertainty or variability as an explanation of the certainty effect.
- #11 In the EUX theory,the same utility is assigned to a wealth of $100, 000, regardless of whether it was reached from a prior wealth of $95,000 or $105,000.
- #13 The theory is developed for simple prospects with monetary outcomes and stated probabilities
- #14 Combination: the prospect (200, .25; 200, .25) will be reduced to (200, .50) Coding & combination & segregation for each prospect separately. Cancellation: one type is the example of problem 10; Cancellation: (200, .20; 100, .50; -50, .30) & (200, .20; 150, .50; -100, .30) (100,.50; -50,.30) & (150, .50; -100, .30).
- #15 Many anomalies of preference result from the editing of prospects. V is defined on prospects, while v is defined on outcomes & V(x,1.0) = V(x) = v(x). For the second equation: the value of a strictly positive or strictly negative prospect equals the value of the riskless component plus the value-difference between the outcomes, multiplied by the weight associated with the more extreme outcome.
- #18 Sub-additivity need not hold for large values of p. Recall that in Problem 8, (6,000, .001) is preferred to (3,000, .002). Hence ∏(.001)/∏(.002) > v(3000)/v(6000)>1/2 by concavity of v.