Hi there.

For one of my statistics courses, I have been given a question about "Equivalence principle" in regard to life insurance. For this question, I have been given a transition probability matrix/Markov chain with state space S={0,1,2,3} whereby 0 = healthy, 1 = ill, 2 = death and 3 = cancellation of insurance plan. 'a' is for the premium the person has to pay. From my understanding of Equivalence principle, this term is defined as the expected value of the premium is equal to the expected value of the pay out from an insurance company, which must be equal to zero. However, generally, how do I go about much the premium will be? I am not an actuary student, so I need someone to explain to me about how Equivalence principle works.

Cheers, your help is very much appreciated.

Edit (extra info - sorry, should have had added this in before)

'a' is for the premium the person has to pay if he is not at all sick during the year. (1-b)a is what the premium is reduced to if the person gets sick, whereby b is the fraction of the year the person is sick, and the person will get $10,000b annual payment when sick.