# What is implied by “No arbitrage” in this example?

Suppose that we are in one period model, where assets are bought (in positive and/or negative values) at $$t=0$$ and are redeemed for their value at time $$t=1$$. Furthermore, suppose that there are three assets: $$A$$, $$S$$, and $$R$$.

Asset $$A$$ is a riskless investment with initial cost of $$90$$ and final payoff of $$100$$. Asset $$S$$ is a risky asset with an initial cost of $$20$$, that returns $$25$$ if state $$\omega_1$$ realizes at $$t=1$$, and returns $$15$$ if state $$\omega_2$$ realizes at $$t=1$$.

All that we know about Asset $$R$$ is that it if $$\omega_1$$ occurs, it returns $$30$$, and if $$\omega_2$$ occurs, it returns $$28$$. Given that there are no arbitrage opportunities, what is the strongest statement we can make about the initial price of Asset $$R$$?

Obviously, the price for one unit of $$R$$ must be bigger than 0. My next inclination was to say that the price of $$R$$ must also be bigger than $$28$$, but when I attempted to prove this via contradiction, I was unable to. Is there an effective strategy for solving this type of question?