No Marginal Arbitrage of the Second Kind for High Production Regimes in Discrete Time Production–Investment Models with Proportional Transaction Costs

21 Pages Posted: 6 Mar 2013

See all articles by Bruno Bouchard

Bruno Bouchard

Université Paris Dauphine - CEREMADE

Adrien Nguyen Huu

Université Paris Dauphine

Date Written: April 2013

Abstract

We consider a class of production–investment models in discrete time with proportional transaction costs. For linear production functions, we study a natural extension of the no‐arbitrage of the second kind condition introduced by Rásonyi. We show that this condition implies the closedness of the set of attainable claims and is equivalent to the existence of a strictly consistent price system under which the evaluation of future production profits is strictly negative. This allows us to discuss the closedness of the set of terminal wealth in models with nonlinear production, functions which may admit arbitrages of the second kind for low production regimes but not marginally for high production regimes.

Keywords: financial markets with transaction costs, nonlinear returns, no‐arbitrage of the second kind, consistent price systems

Suggested Citation

Bouchard, Bruno and Nguyen Huu, Adrien, No Marginal Arbitrage of the Second Kind for High Production Regimes in Discrete Time Production–Investment Models with Proportional Transaction Costs (April 2013). Mathematical Finance, Vol. 23, Issue 2, pp. 366-386, 2013, Available at SSRN: https://ssrn.com/abstract=2229085 or http://dx.doi.org/10.1111/j.1467-9965.2011.00493.x

Bruno Bouchard (Contact Author)

Université Paris Dauphine - CEREMADE ( email )

Place du Marechal de Lattre de Tassigny
Paris Cedex 16, 75775
France

Adrien Nguyen Huu

Université Paris Dauphine

Place du Maréchal de Lattre de Tassigny
Paris, 750016
France

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