Question

Suppose a company charges an annual premium of $100 for an insurance policy for minor injuries. Actuarial studies show that in case of an injury claim, the company will pay out an average of $900 for outpatient care and an average of $3000 for an overnight stay in the hospital.They also determine that, on average, each year there are five claims made that result in outpatient care for every 1000 policies and three claims made that result in an overnight stay out of every 1000 policies. What is expected annual profit of an insurance policy for the company?

Answer 1

Given that on average, each year there are five claims made that result in outpatient care for every 1000 policies

Probability of claim being an outpatient care = 5/1000

= 0.005

given that on avsrage three claims made that result in an overnight stay out of every 1000 policies

Probability of claim being an overnight stay = 3/1000

= 0.003

Probability that there is no claim or no injury = 1 - 0.005 - 0.003

= 1 - 0.008

= 0.992

Which in simple terms is Probability of no minor injury = 0.992

The expected value of insurance policy for the company can be calculated as follow

Type of claim	Probability P(x)	Profit for the Company (x)	x * P(x)
Outpatient care	0.005	= (100 - 900) = -800	0.005 * (-800)
Overnight stay	0.003	= (100 - 3000) = -2900	0.003 * (-2900)
No Injury or claim	0.992	= (100 - 0) = 100	0.992 * 100
			x * P(X) = 86.5

The expected profit of an insurance policy for the company = x * P(X) = $86.5