Gross premiums

Question 1

Gross future loss random variable

Answer 1

The present value of the future outgo minus the present value of the future income

Question 2

The equivalent principle states that

Answer 2

E[Gross future loss] = 0

Which implies that EPV Premiums = EPV benefits + EPV expenses so that in an expected present value context the premiums are equal in value to the expenses and the benefits