Q2. Bob's wealth is $2500. However, he faces a 50% chance of suffering a $900 loss. His utility function is U(w) = √w, Where w is his wealth. a) What is Bob's expected utility? b) What is Bob's cost of risk? c) What is the fair premium an insurer should charge for a full insurance? d) If the insurer set the premium to $500 for a full insurance, will Bob buy it? e) What is the maximum amount Bob would be willing to pay for a full insurance?

Exercise 4: Insurance Fiona has von Neumann-Morgenstern utility function u(x) = VT and initial wealth 640, 000. She faces a 25% chance of losing L = 280, 000. 1. Is Fiona risk averse? 2. What is Fiona's utility if no loss occurs, what is her utility if the loss occurs? What is Fiona's expected utility? 3. What is the cost of fair insurance against the possible loss? Suppose Fiona is able to choose insurance with any coverage z E [0, 1] (i.e. 0 0 C(z) = if z = 0 4. Suppose co = 0 and c1 = 70,000. Is insurance at coverage level z > 0 fair insurance? What coverage level z* would Fiona choose? Explain. 5. Suppose co = 100 and c1 = 70,000. Is insurance at coverage level z > 0 fair insurance? What coverage level z** would Fiona choose? Explain. (Note that co = 100 is an "avoidable fixed cost" which is only paid if she chooses strictly positive insurance coverage. However, the "marginal cost" of additional insurance, c1 = 70,000, is the same as in the previous part.) 6. Suppose co = 100 and…

A risk-averse consumer with $100,000 in wealth faces 0.1 probability of losing half of his wealth within the next year. a. What is the consumer's expected wealth one year from now? b. An insurance company offers our consumer full insurance against the possible loss. What premium must the consumer be charged for the insurance company to expect to break even?   c. Suppose our risk-averse consumer is indifferent between getting $85,000 wealth with certainty and facing the above described uncertain situation. What is the maximum premium that the insurance company will be able to charge this consumer for its full insurance policy?

Q4. An individual with the utility function u(x) = x² owns her wealth of $20,000. An expected profit maximizing company (or risk neutral company) facing the individual can make expected profit greater than $ 19,900. True or False? Explain it. If it is true, show

Use the utility function u = E (r,) – 0.5 A o, where A is the risk aversion parameter and A = 3.5. Use the average annual return on the S&P 500 as E(r,). Use the average annual interest rate on the US Government 10-year treasury bond over the past decade as r Solve for the investor's optimal allocation between the risky and the risk-free asset.

Sarah has a utility function expressed as the square root of wealth (w). Currently, Sarah has an initial wealth of $2000 and faces a potential loss of $1500 with a loss probability of .15. What is Sarah's expected utility if an insurer charges her a pure (actuarially fair) premium? 63.75 41.37 42.13 225

Exercise 5: Insurance Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810,000 and face a 40% chance of losing L = 450, 000. Dave has von Neumann-Morgenstern utility function up(x) = x and Eva has von Neumann-Morgenstern utility function ug (x) = VT. 1. What do you know about Dave's and Eva's risk preferences? 2. What is the most Dave would be willing to pay for complete insurance against the loss? 3. What is the most Eva would be willing to pay for complete insurance against the loss? Suppose they are each able choose insurance with any coverage level z [0, 1] (i.e. 0 0. 6. Is Eva's optimal choice full insurance, i.e. z = 1?

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Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. b) What would be the highest price (premium) that she would be willing to pay for an insurance policy that fully insures her against the flooding damage?