1 a and b. and 2 a-c. please show work

Problem 1: Steven Steel Corporation faces the following loss distribution for annual liability losses: Loss=$$$1,200,000800,000$120,000withprob.0.91withprob.0.01withprob.0.03withprob.0.05 a) Claims are paid at the end of the year, the annual interest rate is 3%, and administrative expenses equal 15% of the expected claim costs and are paid immediately. A profit loading of 4% applies. Find the fair premium for full insurance coverage. b) How is the insurer's investment income affected if the interest rate changes or if the time horizon changes? How would this be reflected in the premium? Solution: a) $48,756.70 b) If the interest rate increases, insurers earn more investment income on every dollar. Therefore, they need to collect a lower premium upfront to break even on the promised indemnity payments. If there is a longer time horizon until claims are paid, insurers carn higher investment income as well because they get to keep the premium dollars for a longer time. This also lowers the required upfront premium. Problem 2: Steven Steel Corporation obtains a liability policy with a $100,000 selfinsured retention and a $1m limit. a) Use an exposure diagram to illustrate both the payment they receive under the insurance policy as well as their retained loss as a function of the annual liability loss. b) Given the loss distribution from Problem 1, what is the expected claim cost under the policy? Compare this to the expected claim cost under full insurance from la). What do you observe and why? c) Under the assumptions from Ia), what is the fair premium for the policy with a $100,000 self-insured retention and a $1m limit? Would you recommend the policy with the provisions or rather the full insurance policy from Problem 1a)? Why