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A unique state price vector does not have to exist for there to be no arbitrage. It sounds like the state price vector in question has infinitely many solutions. Try to reduce the price matrix to row echelon form and show that at least one state price vector exists.


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The negative solution does not satisfy $P(T,T)=P(t,t)=1$


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Apparently this company was traded OTC/Pink sheet (and was already dubious in 1988 see "Precision Imaging Corp" http://babel.hathitrust.org/cgi/pt?id=uiug.30112058759736;view=1up;seq=175). To my knowledge Compustat database doesn't have it neither. My next best guess is to try at your library in some old books like "Walker's Manual" or Moody's. And my last ...



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