Question 1:

Recall the St. Petersburg game. It starts at $2. Toss a coin and if a head appears, thepot doubles. If tails appears, you win the pot at that time and thegame ends.So, if you get H, H, H T, you win $16. The payoff table is,

First head on toss: 1 2 3 4 4 [...] n
Payoff, x $2 $4 $8 $16 $32 $2n

Assume that your utility function is U(x)=√x .

Question 1A. What is the expected monetary value of the game, and what should you be willing to pay to play this game?

Question 1B. Do these values differ? If so, explain why the do.

Question 1C. What is the risk premium you are willing to pay to avoid the uncertainty of the gamble.

Avoiding catastrophic risks

SaveAlot Insurance Co. of Falls Church, VA approaches you for advice on reinsurance protection for their natural hazards class of business. SaveAlot is in the direct insurance business in the Maryland-Virginia region.
SaveAlot'sNet Retention per year for a certain book of policies is $10m. They are now looking to purchase additional reinsurance treaty capacity either on,

(1) a quota share basis of 40% without retention and with a capacity of $50m, or
(2) a surplus share basis with a capacity of $50m, or
(3) an excess of loss basis.

For simplicity, presume the premiumsfor the three proposals for the coming year are $2m, $3m, and $5m,respectively.

Question. If SaveAlot suffers $65m in claims on its book of policies next year, how much would their total loss (including premium) be under the three possible reinsurance options?