1. An insurer has liabilities at the end of the year that are normally distributed with mean of $500 million and standard deviation of $50 million. In contrast to question 3, assets are invested in a risky portfolio with an expected return of 5% and a standard deviation of 10%. Assume that the insurer has assets at the beginning of the year equal to $616 million.Is the probability of assets being greater than liabilities at the end of the year (surplus is positive ) greater than or less than 99%?
2. Find the fair premium for a policy with a $1 million deductible and $20 million limit when the loss distribution is as follows:

0 with prob. 0.80

1 million with prob. 0.10

Loss = 6 million with prob. 0.06

16 million with prob. 0.03

30 million with prob. 0.01

Assume that underwriting and capital costs = $0.4 million, that claim processing (loss adjustment) costs equal 10% of the amount paid in claims, and ignore the time value of money,