What is the arbitrage opportunity in Arrow-Debreu One Period market Model

The one period market model is made of 4 securities(A, B, C, D) and has 4 future states. Assume the market model is complete. and the state prices are (-2, 2, 4, 8).

Given that I dont know the payoff of each security in each state; neither do i know the spot price of each security.

How can I find an arbitrage opportunity?

• is this the exercise the way it was written in the book or are you paraphrasing it ? It seems a bit incomplete to me. Perhaps you could just type it down the way it is written in the text-book or on the exercise sheet – Probilitator Feb 26 '14 at 6:53
• The question is like this. A one period market model is made of 4 securities and has 4 states at time T>0. Assume that the market model is complete and that the state prices are -2, 2, 4 and 8. show that this market is not arbitrage-free by finding an arbitrage opportunity – agent251 Feb 26 '14 at 12:44
• by state prices do you mean a vector $\phi$ with $q=D\phi$ With $q$ being the price vector at $t=0$ , $D$ being the state price matrix (here $4\times 4$) ? – Probilitator Feb 26 '14 at 17:17