Semimartingale Property and Its Connections to Arbitrage


In this paper, we prove the celebrated Bichteler-Dellaccherie Theorem which states that the class of stochastic processes X allowing for a useful integration theory consists precisely of those processes which can be written in the form X = X0 + M + A, where M0 = A0 = 0, M is a local martingale, and A is of finite variation process. We obtain this decomposition rather direct form an elementary discrete-time Doob-Meyer decomposition. By moving to convex combination we obtain a direct continuous time decomposition, which then yield the desired decomposition. We also obtain a characterization of semi-martingales in terms of a variant no free lunch with vanishing risk.

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S. Samura, J. Mao and D. Yao, "Semimartingale Property and Its Connections to Arbitrage," Journal of Mathematical Finance, Vol. 3 No. 2, 2013, pp. 237-241. doi: 10.4236/jmf.2013.32023.

Conflicts of Interest

The authors declare no conflicts of interest.


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