Kindly assist me to solve the following questions. Include clear explanations. Thank you

The aggregate claims arising during each year from a particular type of annual insurance policy are assumed to follow a normal distribution with mean 0.7P and standard deviation 2.0/. where / is the annual premium. Claims are assumed to arise independently. Insurers assess their solvency position at the end of each year. A small insurer with an initial surplus of 10.Im expects to sell 100 policies at the beginning of the coming year in respect of identical risks for an annual premium of 65,000. The insurer incurs expenses of 02P at the time of writing each policy. Calculate the probability that the insurer will prove to be insolvent at the end of the coming year. Ignore interest.A general insurance company is planning to set up a new class of travel insurance. It plans to start the business with f2 million and expects claims to occur according to a Poisson process with parameter 50. Individual claims are thought to have a gamma distribution with parameters o =150 and 1 =14. A premium loading factor of 30% is applied. Explain how each the following changes to the company's model will affect the probability of ultimate ruin: (i) A 28% premium loading factor is applied instead. [1] (ii) Individual claims are found to have a gamma distribution with parameters ( =150 and 1 =1/2. [1] (iii) The Poisson parameter is now believed to be 60. [1] [Total 3]Claims occur according to a compound Poisson process at a rate of 0.2 claims per year. Individual claim amounts, X , have probability function: P(X = 50) = 0.7 P(X = 100) = 0.3 The insurer's surplus at time 0 is 75 and the insurer charges a premium of 120% of the expected annual aggregate claim amount at the beginning of each year. The insurer's surplus at time f is denoted U(t). Find: PLU (2)