Nonequilibrium Geometric No-Arbitrage Principle and Asset Pricing Theorem

We find a novel and intimate correspondence in the present paper between the martingale and one-parameter transformation group and develop a nonequilibrium geometric no-arbitrage principle to a frictional financial market via this correspondence. Further, we achieve a fundamental pricing theorem via a geometric pricing transform (generator). Finally, we derive that the nonequilibrium geometric no-arbitrage is equivalent to NFLVR in a frictionless financial market. In addition, we apply the nonequilibrium geometric no-arbitrage condition to a frictional financial market. At the end of this paper, a numerical example confirms the effectiveness of the nonequilibrium geometric no-arbitrage condition.