An insurance company offers accident insurance for employees. There are two types of policies in the portfolio. All policies are assumed to be independent. The annual number of claims arising from policies of Type 1 can be mod- elled as Poisson(20); the claim amount is always £3000. The annual number of claims arising from policies of Type 2 can be mod- elled as Poisson(25); the claim amount is either £2000 or £3000, with probabilities 0.4 and 0.6, respectively. Calculate the mean and variance of the aggregate annual claims from the portfolio. [10 marks] 4. Your are given: Mean 8 Number of claims Standard deviation 3 3937 Individual losses 10000 As a benchmark, use the normal approximation to determine the prob- ability that the aggregate loss will exceed 150% of the expected loss [10 marks] 5. Gulf Insurance Company has this portfolio of Group Term Life containing 300 policies. Each policy is independent of the other policies. The details are as fol- lows. • There are 200 policies in this portfolio who are factory workers. The probability of death for each insured who is a factory worker is 0.08. The amount of death benefit is uniformly distributed between £1000 and £2000. • There are 100 policies in this portfolio who are executives. The prob- ability of death for each insured who is an executive is 0.05. The amount of death benefit is £10000 for all executives. Let S be the random variable representing the total losses paid during the next year. Calculate: 1. The expected value and variance of claim amount for factory work- ers. [3 marks] 2. The expected value and variance of claim amount for executives. [3 marks]
