CAN YOU PLEASE ADD FORMULAS SO I CAN COMPLETE SIMILAR QUESTIONS ON MY OWN. ?Than

Question

CAN YOU PLEASE ADD FORMULAS SO I CAN COMPLETE SIMILAR QUESTIONS ON MY OWN.
?Thank you!

2. An insurance company's losses of a particular type per year are to a reasonable approximation normally distributed with a mean of $150 million and a standard deviation of $50 million. (Assume that the risks taken on by the insurance company are entirely non-systematic.) The one-year risk-free rate is 5% per annum with annual compounding. Estimate the cost of the following a. A contract that will pay in one year's time 60% of the insurance company's costs on a pro rata basis b. A contract that pays $100 million in one year's time if losses exceed $200 million

Explanation / Answer

a). The losses in millions of dollars are normally distributed with mean 150 and standard deviation 50. The payout from the reinsurance contract is therefore normally distributed with mean 90 and standard deviation 30. Assuming that the reinsurance company feels it can diversifyaway the risk, the minimum cost of reinsurance is

90/1.05 = 85.71 or $85.71 million

b). The probability that losses will be greater than $200 million is the probability that a normallydistributed variable is greater than one standard deviation above the mean. This is 0.1587. The expected payoff in millions of dollars is therefore 0.1587 × 100=15.87 and the value of the contract is

15.87/1.05 = 15.11 or $15.11 million.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.