Consider the following lottery (3600, 0.35; 2700, 0.35; 200, 0.30). Take the reference point to be 1100. Let the value function be v(w) = w^0.50 for the domain of gain and v(w) = −1.5(−w)^0.50 for the domain of loss. Let the weight function be w(p) = p^2. Derive the certainty equivalent of this lottery as per the prospect theory approach? Is this individual risk averse as per the prospect theory approach? this individual risk averse as per the prospect theory approach?
Question
Consider the following lottery (3600, 0.35; 2700, 0.35; 200, 0.30). Take the reference point to be 1100. Let the value function be v(w) = w^0.50 for the domain of gain and v(w) = −1.5(−w)^0.50 for the domain of loss. Let the weight function be w(p) = p^2. Derive the certainty equivalent of this lottery as per the prospect theory approach? Is this individual risk averse as per the prospect theory approach? this individual risk averse as per the prospect theory approach?
Solution
To derive the certainty equivalent of this lottery using the prospect theory approach, we need to calculate the expected value and the weighting function for each outcome.
First, let's calculate the expected value for each outcome:
- For the first outcome (3600, 0.35), the expected value is 3600 * 0.35 = 1260.
- For the second outcome (2700, 0.35), the expected value is 2700 * 0.35 = 945.
- For the third outcome (200, 0.30), the expected value is 200 * 0.30 = 60.
Next, let's calculate the weighted value for each outcome using the weighting function:
- For the first outcome, the weighted value is 1260^0.50 = 35.48.
- For the second outcome, the weighted value is 945^0.50 = 30.74.
- For the third outcome, the weighted value is -1.5 * (-60)^0.50 = -12.25.
Now, let's calculate the certainty equivalent by summing the weighted values: Certainty Equivalent = 35.48 + 30.74 + (-12.25) = 53.97.
Based on the prospect theory approach, an individual is considered risk-averse if the certainty equivalent is lower than the expected value. In this case, the certainty equivalent is 53.97, which is lower than the expected value of 1260. Therefore, this individual is risk-averse as per the prospect theory approach.
Similar Questions
Consider an individual who has the following value function: v ( x )=√(x /2) for gains and v ( x )=-2 √|x| for losses. This individual is facing a lottery which consist of winning Rs. 1600 with a 25% chance, Rs. 400 with a 25% chance, and winning nothing with a 50% chance. The individual counts all outcomes as losses; that is, he takes as his reference point the best possible outcome under consideration. Suppose the weight function is p^2. What will be the expected value/utility of this lottery as per the prospect theory approach? What will be the expected value/utility of this lottery as per the RDU approach? What will be the certainty equivalent of this lottery as per the prospect theory approach?
Consider an individual who has the following value function: v(x) = x^1/2 for gains and v(x) = −2(|x|)^1/2 for losses. This individual is facing a lottery which consist of winning Rs. 25000 with a 25 % chance, Rs. 15000 with a 25 % chance, and losing Rs. 5000 with a 50 % chance. Suppose the probability weight function is p^2. What will be the expected utility of this lottery? What will be the value of this lottery as per the RDU approach? What will be the certainty equivalent of this lottery as per the expected theory approach? What will be the certainty equivalent of this lottery as per the RDU approach?
A.1 If an individual is risk averse, then:i. He prefers any lottery to amounts of money that are certain.ii. The certainty equivalent of a lottery is higher than its expected value.X. The utility function is concave.iv. The utility function is decreasing.
In the story of the Man in the Green Bathrobe, there is oneparticular feature of Prospect Theory that this gambler apparentlyviolates. Which feature?1 point Risk aversion over gains Loss aversionRisk seeking over losses
Risk perception is an individual’s willingness to accept a certain amount of risk.Select one:TrueFalse
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