Risk models

risk models past paper question

Question 40 An insurer wants to model the number of claims arising from storms in a certain region. The number of storms over the period considered, T, is assumed to have a Poisson distribution with parameter u. The parameter y is however unknown but is assumed to be either 10 for a storm without hail or 30 for a storm with hail. The probability of there being hail is 0.2. a) Can the storms be considered independent? Explain. Include the distribution description in your answer. b) Let N, be the number of claims from the storm. It is assumed to be distributed bin(n,p). Is this a good assumption for a distribution? What will have to be considered to implement such a choice? c) If , and p are considered known, derive the mean and variance of the number of claims arising from all the storms over the period considered. Question 41 An insurer models the total claims from lightning strikes during a certain storm. The number of lightning strikes follows the Poisson distribution with parameter a. The value of a is unknown and is assumed to be a realisation from the exponential distribution with known parameter u. (a) Explain why the lightning strikes from this storm cannot be modelled independently. Include the distribution of the number of lightning strikes in your answer. (b) It is assumed that one claim will occur per lightning strike with probability p=0.05. Derive the mean and variance of the number of claims due to lightning strikes arising from this storm. Question 40 An insurer wants to model the number of claims arising from storms in a certain region. The number of storms over the period considered, T, is assumed to have a Poisson distribution with parameter u. The parameter y is however unknown but is assumed to be either 10 for a storm without hail or 30 for a storm with hail. The probability of there being hail is 0.2. a) Can the storms be considered independent? Explain. Include the distribution description in your answer. b) Let N, be the number of claims from the storm. It is assumed to be distributed bin(n,p). Is this a good assumption for a distribution? What will have to be considered to implement such a choice? c) If , and p are considered known, derive the mean and variance of the number of claims arising from all the storms over the period considered. Question 41 An insurer models the total claims from lightning strikes during a certain storm. The number of lightning strikes follows the Poisson distribution with parameter a. The value of a is unknown and is assumed to be a realisation from the exponential distribution with known parameter u. (a) Explain why the lightning strikes from this storm cannot be modelled independently. Include the distribution of the number of lightning strikes in your answer. (b) It is assumed that one claim will occur per lightning strike with probability p=0.05. Derive the mean and variance of the number of claims due to lightning strikes arising from this storm