# Question: consider a market with 123 r 0...

###### Question details

Consider a market with Ω = {ω1,ω2,ω3), r = 0 and one asset S. Suppose that S(0) = 2 and S has claim S̄ = (1,3,3) at time 1. Find all the risk-neutral probability measures on Ω.

I have worked out the risk neutral probability measure for w1, which is 1/2, by using the definition of probability measure EQ(Sn∗(1)) = Sn∗(0) (i.e. p1+3*p2+3*p3=2) and the fact that p1+p2+p3=1. So I'm left with p2+p3=1/2, not sure what to do next.