# The deflator of reinsurance market is unique

How to prove that the deflator $$\phi$$ of the reinsurance market is unique when working in the equilibrium model?

That is, if we have a pricing function $$\pi$$, which satisfies:

$$\pi(Y)=E(\phi Y)$$

Then $$\phi$$ is unique. The pricing function is a function from random variables (claims amounts) to real numbers, and is linear.