(Insurance) Let X = R+. Consider a house owner whose house has a risk of

Question

burning down with probability 0.001. If the house burns down it is worth
$0 otherwise it is worth $1 million. The owner of the house is an expected utility maximizer with a vNM utility function u(x) = x^(1/2) over final wealth. Suppose now that there is an insurance company who may sell full insurance to this agent at a premium p. The contract is of the form: If the agent pays $p million then the
insurance company will pay the agent $1 million in case his house burns down. The insurance company does not pay back the p later, whether the house burns down or not.
(a) How do you describe the risk attitudes of the house owner?
(b) For which values of p, would the owner of the house be willing to buy the insurance?
(c) If the insurance company maximizes expected profits and knows (b), what
premium p* would it set? What are the company’s expected profits?