Question

suppose a company charges an annual premium of $110 for 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 each outpatient care in an average of $3000 for an overnight stay in the hospital. they also determine that on average each year there are five claims made as a result in outpatient care for every 1000 policies in three claims made that result in an overnight stay out of every 1000 policies. what is the expected annual profit of an insurance policy for the company??

Answer 1

Event	Amount (X)	Probability (p)	X*p
outpatient care	110 - 900 = -790	5/1000=0.005	-790*0.005 = -3.95
overnight stay	110 - 3000 = 2890	3/1000 = 0.003	-2890*0.003 = -8.67
No claim	110	1-0.005-0.003 = 0.992	110*0.992 = 109.12

Expected value to the company per claim = sum(X*p) = 109.12 - 8.67 - 3.95

Expected value to the company per claim = 96.5

Expected value to the company per 1000 claim = 96.5*1000

Expected value to the company per 1000 claim = $96500