If you are interested, this isnothow premiums on life contracts are actually set. Life contracts are normally long term so you need to account for the investment returns that you will make on the premiums, as well as administrative expenses and a profit margin.

However, since you aren't an actuarial student you can probably forget about that. Your version of the equivalence principle says that the Premium should be equal to the expected value of claims under the contract. This means that, on average, the premiums for a large group of independant contracts will be enough to cover the total claim value. it is an application of the Law of Large numbers.

To do the calculation, you need more information than you have given. Most importantly

1) How many periods the contract runs for

2) How the premium is paid (lump sum at the start? regularly while alive?)

Once you know those two things, use normal methods with markov chains to calculate

1) The expected premium value at outset

2) The chance of a claim occuring during the contract = 1- P(survives to end)

3) The expected claim value at outset (= cover_level * chance_of_claim_at_any_point_in_contract)

Since you have not given the information, here is an example with made up figures.

2 period markov chain. Sum assured S. Lump sum premium P, paid at outset.

States = (alive,dead,cancelled)

Transition matrix

Given that the life starts in state a, the probabilities after 2 states are

at time 1:

P(alive) = 0.8

P(dead) = 0.1

P(cancelled) = 0.1

at time 2:

P(alive) = 0.64

P(dead) = 0.18

P(cancelled) = 0.18

So P(claim) = 0.18

E(claim value) = 0.18S

Equivalence Principle: E(claim value) = E(Premiums)

0.18S = P