TY - JOUR
T1 - Arbitrage and approximate arbitrage
T2 - The fundamental theorem of asset pricing
AU - Wong, Bernard
AU - Heyde, C. C.
PY - 2010/4
Y1 - 2010/4
N2 - We consider an incomplete market model where asset prices are modelled by Ito processes, and derive the first fundamental theorem of asset pricing using standard stochastic calculus techniques. This contrasts with the sophisticated functional analytic theorems required in the comprehensive works of F. Delbaen and W. Schachermayer (1993) No Arbitrage and the Fundamental Theorem of Asset Pricing, pp. 37-38; Math. Finance 4 (1994), pp. 343-348; Math. Ann. 300 (1994), pp. 464-520; Ann. Appl. Probab. 5 (1995), pp. 926-645 and Proc. Sympos. Appl. Math. 57 (1999), pp. 49-58, and the comparative lack of transparency of the associated technical conditions. An additional benefit is that a clear relationship between no arbitrage and the existence of equivalent local martingale measures is also presented.
AB - We consider an incomplete market model where asset prices are modelled by Ito processes, and derive the first fundamental theorem of asset pricing using standard stochastic calculus techniques. This contrasts with the sophisticated functional analytic theorems required in the comprehensive works of F. Delbaen and W. Schachermayer (1993) No Arbitrage and the Fundamental Theorem of Asset Pricing, pp. 37-38; Math. Finance 4 (1994), pp. 343-348; Math. Ann. 300 (1994), pp. 464-520; Ann. Appl. Probab. 5 (1995), pp. 926-645 and Proc. Sympos. Appl. Math. 57 (1999), pp. 49-58, and the comparative lack of transparency of the associated technical conditions. An additional benefit is that a clear relationship between no arbitrage and the existence of equivalent local martingale measures is also presented.
KW - Arbitrage
KW - Equivalent local martingale measures
KW - Local martingale
UR - http://www.scopus.com/inward/record.url?scp=77951737277&partnerID=8YFLogxK
U2 - 10.1080/17442500903251824
DO - 10.1080/17442500903251824
M3 - Article
SN - 1744-2508
VL - 82
SP - 189
EP - 200
JO - Stochastics
JF - Stochastics
IS - 2
ER -