Finitely Additive Probabilities and the Fundamental Theorem of Asset Pricing
By Constantinos Kardaras. 2009
75 citations recorded by the source corpus.
This work aims at a deeper understanding of the mathematical implications of the economically-sound condition of absence of arbitrages of the first kind in a financial market. In the spirit of the Fundamental Theorem of Asset Pricing (FTAP), it is shown here that the absence of arbitrages of the first kind in the market is equivalent to the existence of a finitely additive probability, weakly equivalent to the original and only locally countably additive, under which the discounted wealth processes become “local martingales”. The aforementioned result is then used to obtain an independent proof of the classical FTAP, as it appears in Delbaen and Schachermayer (Math. Ann. 300:463–520, 1994). Finally, an elementary and short treatment of the previous discussion is presented for the case of continuous-path semimartingale asset-price processes.
Subfields: Economics and Econometrics, Finance
View Paper: https://www.semanticscholar.org/paper/85ca2e7be96df9012142c3798d2f5bc28099d2ce
How researchers see this paper
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In Economics and Econometrics
- Bruno Bouchard
- Marcel Nutz
- Sara Biagini
- Constantinos Kardaras
- Emmanuel Gobet
- Huyen Pham
- Adrien Richou
- Shige Peng
In Finance
- Bruno Bouchard
- Marcel Nutz
- Sara Biagini
- Constantinos Kardaras
- Daniel Bartl
- Nizar Touzi
- Shige Peng
- Ariel Neufeld
Citations in the corpus
- ROBUST FUNDAMENTAL THEOREM FOR CONTINUOUS PROCESSES (2014, methodology): “NA1(P) implies QP 6= ∅, for arbitrary but fixed P ∈ P. Thus, we are essentially in the realm of classical stochastic analysis and finance; in particular, we may use the tools in the Appendix as well as [26, 27]. Define Xsimp,P as the class of all processes of the form Xx,H for x∈ R+ and H∈ Hsimp,P(x). ”
- HEDGING UNDER ARBITRAGE (2010, unknown): “and Kardaras, 2007, Proposition 3.2), which again yields an ELMM corresponding exactly to the one discussed in this section. Another point of view, which we do not take here, is the recent insight by Kardaras (2010) on the equivalence of NUPBR and the existence of a finitely additive probability meas”