Question: A friend of yours issues a pair of coupons on a binary uncertainty. Each coupon pays an amount equal to $ 10 if a certain outcome occurs. For example, one coupon pays $ 10 if the stock market goes up, and the other pays $10 if the stock market goes down. In other words, a coupon pair will always pay its holder an amount of $10, since we know that exactly one outcome will occur and the bearer will always get paid $10. (Ignore the case that the stock market index remains the same.)
I. Decision maker 1 is risk-averse (risk tolerance equals $20) and believes the stock market will go up with a probability of 0.8.
II. Decision maker 2 is risk-neutral and believes the stock market will go up with a probability of 0.7.
a. What is decision maker 1's PIBP for the coupon pair?
b. After some thought, decision maker 1 says he is risk-neutral. You are called to design the pricing and selling schemes for the two coupons. Which decision maker will you sell each coupon to? What is the maximum profit you can generate for your friend?