An insurance company has a portfolio of policies for which claims occur as a Poisson process...

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An insurance company has a portfolio of policies for which claims occur as a Poisson process at a rate of 50 claims per year. The individual claim amounts in £s follow a log-normal distribution with parameters µ = 5 and o² = 1. The insurer includes a premium loading of 15% on its premiums for this portfolio. a) Find the initial capital required in order to ensure that the probability of ruin at the end of the first year is 2.5%. You should assume that the aggregate claim amount for a year is approximately normally distributed. b) The insurance company decides to reinsure 30% of each risk in the portfolio by taking out proportional reinsurance with a reinsurer that loads its premiums by 25%. Find the new level of initial capital required to ensure that the probability of ruin at the end of the first year is still 2.5%. An insurance company has a portfolio of policies for which claims occur as a Poisson process at a rate of 50 claims per year. The individual claim amounts in £s follow a log-normal distribution with parameters µ = 5 and o² = 1. The insurer includes a premium loading of 15% on its premiums for this portfolio. a) Find the initial capital required in order to ensure that the probability of ruin at the end of the first year is 2.5%. You should assume that the aggregate claim amount for a year is approximately normally distributed. b) The insurance company decides to reinsure 30% of each risk in the portfolio by taking out proportional reinsurance with a reinsurer that loads its premiums by 25%. Find the new level of initial capital required to ensure that the probability of ruin at the end of the first year is still 2.5%.

Answer rating: 100% (QA)

To find the initial capital required to ensure a specific probability of ruin we need to calculate the ruin probability using the classical risk model In this case we can use the aggregate claim amoun... View the full answer