Question

ABC Insurance Company insures properties along the Gulf Coast of the United States. Statutory reserves are liabilities that the insurance company is legally required to maintain on its balance sheet with respect to expected future claims against the company for insured losses. To assist ABC in setting its reserves, we are asked to provide actuarial guidance. Given that the historical average rate of occurrence of a major hurricane along the Gulf Coast is two per year, find the following:

1. The probability of 3 major hurricanes in a year.
2. The probability of at least 2 major hurricanes in a year.
3. The probability of less than 5 major hurricanes in five years.

Answer 1

here we use poisson distribution with parameter λ=2

and P(X=x)=exp(-λ)*λ^x/x!

(a)P(X=3)=0.1804 ( using ms-excel=POISSON(3,2,0))

(b)P(at least 2)=P(X>=2)=1-P(X<2)=1-P(X<=1)=1-(P(X=0)+P(X=1))=1-(0.1353+0.2707)=0.5940

(P(X=0))=0.1353 (using ms-excel =POISSON(0,2,0))

P(X=1)=0.2707 ( using ms-excel =POISSON(1,2,0))

(c) in 5 year expected number of hurricane would be 5*2=10 and

now we use poisson distribution with parameter λ=10

probability of less than 5 major hurricanes in five years=(P(X<5)=P(X<=4)=0.0293(using ms-excel=POISSON(4,10,1))