An insurance company has an insurance policy where the loss amount follows a gamma distribution with = 2 and = 1000.

1. An insurance company has an insurance policy where the loss amountfollows a gamma distribution with α= 2 and θ= 1000. Calculate theexpected payment per claim if the company introduces a deductible of d.2. The severity of a loss on a car insurance policy follows a Pareto distributionwith α= 3 and θ= 3000. Calculate the loss eliminatrion ratio of adeductible of $1,000.3. An insurance company has a policy where losses follow a Weibull distribu-tion with r= 0.5 and θ= 6000. The company’s risk management divisiondecides that the TVaR at the 95% level, for this policy needs to be reducedto $75,000. What policy limit should the company put on the policy toachieve this?(i) $84,400 (ii)$96,300 (iii) $122,000 (iv) $147,0004. For a certain insurance policy, losses follow a gamma distribution with α= 7 and θ= 3000. The deductible is set to achieve a loss eliminationratio of 20%.(a) Calculate the deductible(i) 1500(ii) 2700(iii) 3300(iv) 4200(b) Two years later, there has been uniform ination of 10%, and the company is considering changing the deductible. What is the new losselimination for the current deductible after this 10% ination?5. A certain insurance policy has losses following a Burr distribution with r= 0.6, α= 2 and θ= 4000. There is a deductible of $2,000, and thenumber of claims under the policy follows a negative binomial distributionwith r = 8 and β= 1.3. What would the distribution of the number ofclaims be if the company reduces the deductible to $1,000?Note: If u can answer 4 of the questions on time, i will rate u.

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