Frontiers of Mathematics in China >

2014 , Vol. 9 >Issue 4: 929 - 946

DOI: https://doi.org/10.1007/s11464-014-0406-2

RESEARCH ARTICLE

A comparison of two no-arbitrage conditions

  • Miao WANG 1 ,
  • Jiang-Lun WU , 1,2
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  • 1. Department of Mathematics, Swansea University, Swansea SA2 8PP, UK
  • 2. School of Mathematics, Northwest University, Xi’an 710127, China

Received date: 05 Apr 2014

Accepted date: 28 May 2014

Published date: 20 Aug 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： No free lunch with vanishing risk condition; no good deal condition; extension theorem; fundamental theorem; equivalent martingale measures

Cite this article

Miao WANG , Jiang-Lun WU . A comparison of two no-arbitrage conditions[J]. Frontiers of Mathematics in China, 2014 , 9(4) : 929 -946 . DOI: 10.1007/s11464-014-0406-2

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Albeverio S, Di Nunno G, Rozanov Y A. Price operators analysis in Lp space. Acta Appl Math, 2005, 89: 85-108

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

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