A comparison of two no-arbitrage conditions

Abstract

We give a comparison of two no-arbitrage conditions for the fundamental theorem of asset pricing. The first condition is named as the no free lunch with vanishing risk condition and the second the no good deal condition. We aim to derive a relationship between these two conditions.

Keywords

No free lunch with vanishing risk condition / no good deal condition / extension theorem / fundamental theorem / equivalent martingale measures

References

[1] Albeverio S, Di Nunno G, Rozanov Y A. Price operators analysis in L_p space. Acta Appl Math, 2005, 89: 85-108

[2] Bion-Nadal J, Di Nunno G. Dynamic no-good-deal pricing measures and extension theorems for linear operators on L-infinity. Finance Stoch, 2013, 17(3): 587-613

[3] Cherny A. Generalized arbitrage pricing model. In: Séminaire de Probabilités XL. Lecture Notes in Math, Vol 1899. Berlin: Springer-Verlag, 2007, 415-481

[4] Cocharane J H, Saa Requejo J. Beyond arbitrage: Good deal asset price bounds in incomplete markets. The Journal of Political Economy, 2000, 108: 1-22

[5] Delbaen F, Schachermayer W. A general version of the fundamental theorem of asset pricing. Math Ann, 1994, 300: 463-520

[6] Delbaen F, Schachermayer W. The fundamental theorem of asset pricing for unbounded stochastic processes. Math Ann, 1998, 312: 215-250

[7] Delbaen F, Schachermayer W. What is a free lunch? Notices Amer Math Soc, 2004, 51(5): 526-528

[8] Delbaen F, Schachermayer W. The Mathematics of Arbitrage. Springer Finance. Berlin: Springer-Verlag, 2006

[9] Föllmer H, Schied A. Stochastic Finance. Berlin: Walter de Gruyter, 2002

[10] Øsendal B. Stochastic Differential Equations. 6th ed. Berlin: Springer-Verlag, 2003

[11] Roux A. The fundamental theorem of asset pricing in the presence of bid-ask and interest rate spreads. J Math Econom, 2011, 47: 159-163

[12] Shiryaev A N, Cherny A. Vector stochastic integrals and the fundamental theorems of asset pricing. Proc Steklov Inst Math, 2002, 237: 6-49

[13] Truman A, Wang F-Y, Wu J-L, Yang W. A link of stochastic differential equations to nonlinear parabolic equations. Sci China Math, 2012, 55(10): 1971-1976

[14] Williams R J. Introduction to the Mathematics of Finance. Graduate Studies in Mathematics 72. Providence: Amer Math Soc, 2006

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Higher Education Press and Springer-Verlag Berlin Heidelberg