Show that there are no arbitrage opportunities in this, Financial Management

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Show that there are no arbitrage opportunities in this

Consider two stocks, A and B. For three possible states (w1,w2,w3), the payoff of stocks after year would be as the following:

A: w1: 8 w2: 4 w3: 3

B: w1: 1 w2: 1 w3: 1

The prices of stocks at current time are 5 and 1, respectively.

Show that there are no arbitrage opportunities in this economy. Then, give possible two sets of state prices.

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