Hi

Can you help me with the following, i think it is pretty easy but I don't get it:

Consider a discrete one period model of the financial market. We have a risk-free bond and a stock. The bond hast at time 0 a value of 1 and at time 1 , , , the stock has at time 0 a value of 3 and with positive probability one of the three values (3 possible states) . so we have the following equation system:

The question is to determine all interest rates for which there is no arbitrage and to give an arbitrage opportunity for one of the other .

In a one-period model, I normally look at the equation sytem and determine if we have a unique solution, but how can this be done in this example?

Thank you