Question 4 Individual losses on a portfolio of insurnace policies in 2020

QUESTION 4 (8 marks) Individual losses on a portfolio of insurance policies in 2020 are assumed to follow an exponential distribution with mean parameter 6. In 2021, individual loss amounts have increased by 5% (so that a loss incurred in year 2021 is 5% greater than an equivalent loss incurred in year 2020). Over both the calendar years 2020 and 2021 the insurer had in place an individual Excess of Loss reinsurance arrangement with a retention level of $1800. Claims paid by the insurer were: . 2020: 3 amounts equal to the retention level and 15 claims less than the retention level. The 15 claims less than the retention level sum to $20,000. . 2021: 8 amounts equal to the retention level and 17 claims less than the retention level. The 17 claims less than the retention level sum to $23,000. Assume that we wish to nd the maximum likelihood estimate of 6 using all the 2020 and 2021 claims paid by the insurer (i.e., the combined data). Find the maximum likelihood estimate of 6