×

The fundamental theorem of asset pricing for continuous processes under small transaction costs. (English) Zbl 1239.91190

The question of identification of the necessary and sufficient conditions for proving a version of the fundamental theorem of asset pricing for arbitrary small transaction costs is addressed. In continuous-time setting, a notion of absence of arbitrage admitting a clear-cut economic interpretation to the existence of consistent price system, which correspond to equivalent martingale measure in the frictionless case, is studied. A comparison between numeraire-free and numeraire-based notions of admissibility is provided, and the corresponding martingale and local martingale properties for the consistent price systems are stated as well.

MSC:

91G80 Financial applications of other theories
91B25 Asset pricing models (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Campi L., Schachermayer W.: A super-replication theorem in Kabanov’s model of transaction costs. Fin Stochast 10, 579–596 (2006) · Zbl 1126.91024
[2] Cheridito P.: Arbitrage in fractional Brownian motion models. Fin Stochast 7, 533–553 (2003) · Zbl 1035.60036
[3] Cherny, A.: General arbitrage pricing model: transaction costs. In: Séminaire de Probabilités XL. Lecture Notes in Mathematics 1899, pp. 447–462. Springer, Berlin (2007) · Zbl 1322.91052
[4] Cvitanić J., Karatzas I.: Hedging and portfolio optimization under transaction costs: a martingale approach. Math Fin 6, 133–165 (1996) · Zbl 0919.90007
[5] Davis M.H.A., Norman A.R.: Portfolio selection with transaction costs. Math Oper Res 15, 676–713 (1990) · Zbl 0717.90007
[6] Delbaen F., Schachermayer W.: A general version of the fundamental theorem of asset pricing. Math Ann 300, 463–520 (1994) · Zbl 0865.90014
[7] Delbaen F., Schachermayer W.: The no-arbitrage property under a change of numéraire. Stochast Stochast Rep 53, 926–945 (1995) · Zbl 0847.90013
[8] Delbaen F., Schachermayer W.: The Mathematics of Arbitrage. Springer Finance Series. Springer, Berline (2006) · Zbl 1106.91031
[9] Guasoni P.: No arbitrage with transaction costs, with fractional brownian motion and beyond. Math Fin 16, 569–582 (2006) · Zbl 1133.91421
[10] Guasoni P., Rásonyi M., Schachermayer W.: Consistent price systems and face-lifting pricing under transaction costs. Ann Appl Probab 18, 491–520 (2008) · Zbl 1133.91422
[11] Harrison J.M., Kreps D.M.: Martingales and arbitrage in multiperiod securities markets. J Econ Theory 20, 381–408 (1979) · Zbl 0431.90019
[12] Harrison J.M., Pliska S.R.: Martingales and stochastic integrals in the theory of continuous trading. Stochast Process Appl 11, 215–260 (1981) · Zbl 0482.60097
[13] Jacod J., Shiryaev A.: Limit Theorems for Stochastic Processes. Springer, Berlin (1987) · Zbl 0635.60021
[14] Jouini E., Kallal H.: Martingales and arbitrage in securities markets with transaction costs. J Econ Theory 66, 178–197 (1995) · Zbl 0830.90020
[15] Kabanov Yu.M.: Hedging and liquidation under transaction costs in currency markets. Fin Stochast 3, 237–248 (1999) · Zbl 0926.60036
[16] Kabanov Yu.M., Last G.: Hedging under transaction costs in currency markets: a continuous-time model. Math Fin 12, 63–70 (2002) · Zbl 1008.91049
[17] Kabanov, Yu. M., Stricker, Ch.: Hedging of contingent claims under transaction costs. Advances in Finance and Stochastics. Essays in honour of Dieter Sondermann. In: Sandman, K., Schönbucher, Ph. (eds.), pp. 125–136. Springer, Berlin (2002)
[18] Kabanov Yu.M., Rásonyi M., Stricker Ch.: No-arbitrage criteria for financial markets with efficient friction. Fin Stochast 6, 371–382 (2002) · Zbl 1026.60051
[19] Kreps D.M.L: Arbitrage and equilibrium in economies with infinitely many commodities. J Math Econ 8, 15–35 (1981) · Zbl 0454.90010
[20] Protter, Ph.E.: Stochastic integration and differential equations, 2nd edn. Applications of Mathematics 21, Springer, Berlin (2004) · Zbl 1041.60005
[21] Rogers L.C.G.: Arbitrage with fractional Brownian motion. Math Fin 7, 95–105 (1997) · Zbl 0884.90045
[22] Schachermayer W.: Martingale measures for discrete time processes with infinite horizon. Math Fin 4, 25–55 (1994) · Zbl 0893.90017
[23] Schachermayer W.: The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time. Math Fin 14, 19–48 (2004) · Zbl 1119.91046
[24] Sin, C.A.: Strictly local martingales and hedge rations on stochastic volatility models. PhD Thesis, Cornell University (1996)
[25] Stricker, Ch., Yan, J.-A.: Some remarks on the optional decomposition theorem. Séminaire de Probabilités, XXXII, Lecture Notes in Mathematics 1686, pp. 56–66. Springer, Berlin (1998) · Zbl 0910.60037
[26] Xia J.M., Yan J.A.: Some remarks on arbitrage pricing theory. In: Yong, J.M. (eds) Recent Developments in Mathematical Finance (Shanghai 2001), pp. 218–227. World Scientific, River Edge (2002) · Zbl 1029.91038
[27] Yan, J.-A.: A Numeraire-free and original probability based framework for financial markets. In: Proceedings of the International Congress of Mathematicians Vol. III (Beijing 2002). pp. 861–871. Higher Education Press, Beijing (2002) · Zbl 1005.60058
[28] Yan J.-A.: A new look at the fundamental theorem of asset pricing. J Korean Math Soc 33, 659–673 (1998) · Zbl 0924.60015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.