Suppose a $2,000,000 loss occurs randomly with a 1/200 chance. What is the actuarially fair premium? a. $20,000 b. $200,000 c. $10,000 d. $2,000,000
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Suppose a $2,000,000 loss occurs randomly with a 1/200 chance. What is the actuarially fair premium?
a. $20,000
b. $200,000
c. $10,000
d. $2,000,000
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- Suppose that the probability of breaking a collar bone is p = .05 and the cost of breaking a collar bone is $1,000. What is the actuarially fair price for insurance against breaking your collarbone?David is an expected-utility maximizer that likes to drive fast (and reckless at times), so his probability of an accident is 2/3. David’s preferences over wealth are u(w) = √?. Suppose that David’s initial wealth is $100. If David has an accident, he incurs a $51 loss. How much is the risk premium David willing to pay to be as well off in case of accident or not?Five of ten people earn $0, four earn $100, and one loses $100. What is the expected payoff? What is the variance of the payoff?
- If a risk‐neutral individual owns a home worth $200,000 and there is a three percent chance the home will be destroyed by fire in the next year, then we know that:a) He is willing to pay much more than $6,000 for full cover.b) He is willing to pay much less than $6,000 for full cover.c) He is willing to pay at most $6,000 for full cover.d) None of the above are correct.e) All of the above are correct.Setup from Question 1) An expected utility maximiser owns a car worth £60000 and has a bank account with £20000. The money in the bank is safe, but there is a 50% probability that the car will be stolen. The utility of wealth for the agent is u(y)=ln(y) and they have no other assets. Setup from question 2)Consider the setup from Question 1. A risk-neutral insurance company is willing to insure the car at the premium of π=£2/3 for every one pound of coverage. Question 3:A risk-averse manager is considering a project that will cost £100. There is a 10 percent chance the project will generate revenues of £100, an 80 percent chance it will yield revenues of £50, and a 10 percent chance it will yield revenues of £500. Should the manager adopt the project? Explain. What will a risk-neutral and risk-loving manager do in the same situation?
- Dr. Gambles has a utility function given as U(w)=In(w). Due to the pandemic affecting his consulting business, Dr Gambles faces the prospect of having his wealth reduced to £2 or £75,000 or £100,000 with probabilities of 0.15, 0.25, and 0.60, respectively. Suppose insurance is available that will protect his wealth from this risk. How much would he be willing to pay for such insurance?Burger Prince Restaurant is considering the purchase of a $100,000 fire insurance policy. The fire statistics indicate that in a given year the probability of property damage in a fire is as follows: Fire Damage $100,000 $75,000 $50,000 $25,000 $10,000 $0 Probability .006 .002 .004 .003 .005 .980 If Burger Prince was risk neutral, how much would they be willing to pay for fire insurance? If Burger Prince has the utility values given below, approximately how much would they be willing to pay for fire insurance? Loss $100,000 $75,000 $50,000 $25,000 $10,000 $5,000 $0 Utility 0 30 60 85 95 99 100PROBLEM (4) A homeowner with expected utility preferences with u(x)= sqare root x owns a house worth $490k. There is a probability p that she will experience a house fire, in which case the damages will cost $240k. A risk-neutral insurance company asks for an insurance premium of $10k in return for covering the damages fully in case of a fire. (a) What should p be so that the homeowner is willing to insure her house? (b) What should p be so that the insurance company is willing to offer insurance?
- Any risk-averse individual would always (Select all that applies) Group of answer choices a) take a 20% chance at $100 rather than a sure $20. b) take a sure $20 rather than a 20% chance at $100. c) take a sure $2 rather than a 50% chance at $4 and a 50% chance at losing $1. d) take a 50% chance at $5 and a 50% chance at losing $1 rather than a sure $1.Leora has a monthly income of $20,736. Unfortunately, there is a chance that she will have an accident that will result in costs of $10,736. Thus leaving her an income of only $10,000. The probability of an accident is 0.5. Finally assume that her preferences over income can be represented by the utility function u(x) = 2ln(x).a) What is the expected income? What is Leora’s expected utility (you may leave in log form)? b) What is the certainty equivalent to her situation? What is the risk premium associated with her situation?c) What is the maximum that Leora would be willing to pay for a full insurance policy?d) Illustrate her expected utility, expected wealth, certainty equivalent, the risk premium and her willingness to pay for a full insurance policy in a diagram.Consider an insurance contract with the premium r=$200 and payout q=$800. a.) John has healthy-state income IH = $900 and sick-state income IS = $100. He has probability of illness p = 0.2. Is the contract fair and/or full for John? What is John’s expected income WITHOUT this insurance contract? What is John’s expected income WITH this insurance contract?