ASB-3313 FINANCIAL ECONOMICS
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
ASB-3313 FINANCIAL ECONOMICS
Question 1
a) Consider the following four lotteries:
Lottery A: 40% chance of winning £40,000; 10% chance of winning £20,000, £0 otherwise Lottery B: 30% chance of winning £40,000; 30% chance of winning £20,000, £0 otherwise Lottery C: 50% chance of winning £40,000; 40% chance of winning £20,000, £0 otherwise
Lottery D: 60% chance of winning £40,000; 20% chance of winning £20,000, £0 otherwise
If an individual prefers lottery A to lottery B, and prefers lottery C to lottery D; prove rigorously whether or not their preferences conform with the Independence Axiom of Expected Utility Theory. [50%]
b) Critically evaluate the claim that the Allais paradox fatally undermines Expected Utility Theory. [50%]
Question 2
a) Consider the following four lotteries:
Explain the concepts of first-order and second-order stochastic dominance. Prove robustly
for each lottery whether it first-order or second-order stochastically dominates any of the
other lotteries. [50%]
b) To what extent do Mean-Variance preferences conform with first-order stochastic dominance? Explain your answer fully. [50%]
Question 3
a) Imagine you are considering whether to buy a stock. The value of the stock tomorrow is represented by a binary random variable 
= (0, 1 − 
; 100, 
) , where 
is the probability of high value (
= 100) whilst 1 − 
is the probability of low value (
= 0). It costs 50 to buy the stock.
i. Graph the optimal expected profits as a function of 
and show that it is convex.
[25%] Assume now that there exists a signal which perfectly reveals the true state of the world. I.e., the signal is good (
) whenever the future value is 
= 100, and bad (
) whenever the future value is 
= 0.
ii. Graph the value of this information as function of 
. [25%]
b) In what circumstances, in general, might the value of information not be positive? Illustrate your answer with potential examples from theory or the real world. [50%]
Question 4
a) Assume a perfectly competitive insurance market, but where there is a transaction cost of 10% (
= 0. 1). Anest has utility function 
(
) = √
and initial wealth of £10,000. She faces a potential loss of £4,000 with probability 1⁄4.
i. What insurance premium will Anest have to pay if she chooses to cover 80% of her potential loss (
= 0.8)? [10%]
ii. What is the optimal proportion, 
, of her loss that Anest should choose to cover? [15%]
iii. Calculate Anest’s expected utility at her optimal value of 
, and compare it to her expected utility when 
= 0 and when 
= 1. [10%]
iv. If Anest’s initial wealth had instead been £5,000, what would her optimal 
have been. Why does it differ in this way? [15%]
b) Explain the conditions under which a pooling or separating equilibrium exists in a competitive insurance market with adverse selection? [50%]
Please ensure that you have answered 2 questions in total
Each question carries equal weight
Diwedd / End
2021-12-24