Skip to main content
Log in

A general version of the fundamental theorem of asset pricing

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • Ansel, J.P., Stricker, C. (1992): Couverture des actifs contingents. (Preprint)

  • Ansel, J.P., Stricker, C. (1993): Lois de martingale, densités et décomposition de Föllmer-Schweizer. Ann. Inst. Henri Poincaré28, 375–392

    Google Scholar 

  • Artzner, Ph., Heath, D. (1990): Completeness and non unique pricing. Strasborg: Université Louis Pasteur (Preprint)

  • Back, K., Pliska, S. (1991): On the fundamental theorem of asset pricing with an infinite state space. J. Math. Econ.20, 1–18

    Google Scholar 

  • Banach, S. (1932): Théorie des opérations linéaires. Monogr. Mat., Warsawa 1. Reprint by Chelsea Scientific Books (1963)

  • Black, F., Scholes, M. (1973): The pricing of options and corporate liabilities. J. Pol. Econ.81, 637–654

    Google Scholar 

  • Chou, C.S., Meyer, P.A., Stricker, S. (1980): Sur les intégrales stochastiques de processus prévisibles non bornés. In: Azéma, J., Yor, M. (eds.) Séminaire de probabilités XIV. (Lect. Notes Math., vol. 784, pp. 128–139) Berlin, Heidelberg New York: Springer

    Google Scholar 

  • Dalang, R.C., Morton, A., Willinger, W. (1989): Equivalent martingale measures and no-arbitrage in stochastic securities market models. Stochastics and Stochastics Rep.29, 185–202

    Google Scholar 

  • Delbaen, F. (1992): Representing martingale measures when asset prices are continuous and bounded. Math. Finance2, 107–130

    Google Scholar 

  • Delbaen, F., Schachermayer, W. (1993): Arbitrage and free lunch with bounded risk for unbounded continuous processes. (to appear)

  • Delbaen, F., Schachermayer, W. (1993b): Forthcoming paper on Bes3 (1) process

  • Delbaen, F., Schachermayer, W. (1994): An inequality for the predictable projection of an adapted process. (in preparation)

  • Dellacherie, C., Meyer, P. (1980): Probabilités et potentiel, chap. V à VIII, théorie des martingales. Paris: Hermann

    Google Scholar 

  • Diestel, J. (1975): Geometry of Banach spaces-selected topics. (Lect. Notes Math., vol. 485) Berlin Heidelberg New York: Springer

    Google Scholar 

  • Dothan, M. (1990): Prices in financial markets. New York: Oxford University Press

    Google Scholar 

  • Duffie, D. (1992): Dynamic asset pricing theory. Princeton: Princeton University Press

    Google Scholar 

  • Duffie, D., Huang, C.F. (1986): Multiperiod security markets with differential information. J. Math. Econ.15, 283–303

    Google Scholar 

  • Dybvig, P., Ross, S. (1987): Arbitrage. In: Eatwell, J., Milgate, M., Newman, P. (eds.) The new Palgrave dictionary of economics, vol. 1, pp. 100–106, London: Macmillan

    Google Scholar 

  • Émery, M. (1979): Une topologie sur l'espace des semimartingales. In: Dellacherie, C. et al. (eds.) Séminaire de probabilités XIII. (Lect. Notes Math. vol. 721, pp. 260–280) Berlin Heidelberg New York: Springer

    Google Scholar 

  • Émery, M. (1980): Compensation de processus non localement intégrables. In: Azéma, J., Yor, M. (eds.) Séminaire de probabilités XIV (Lect. Notes Math., vol. 784, pp. 152–160) Berlin Heidelberg New York: Springer

    Google Scholar 

  • Föllmer, H., Schweizer, M. (1991): Hedging of contingent claims under incomplete information. In: Davis M.H.A., Elliott, R.J., (eds.) Applied stochastic analysis. (Stochastic Monogr., vol. 5, pp. 389–414) London New York: Gordon and Breach

    Google Scholar 

  • Grothendieck, A. (1954): Espaces vectoriels topologiques. São Paulo: Sociedade de Matematica de Sào Paulo

    Google Scholar 

  • Harrison, M., Kreps, D. (1979): Martingales and arbitrage in multiperiod security markets. J. Econ. Theory20, 381–408

    Google Scholar 

  • Harrison, M., Pliska, S. (1981): Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes Appl.11, 215–260

    Google Scholar 

  • Huang, C.F., Litzenberger, R. (1988): Foundations for financial economics. Amsterdam: Noord Holland

    Google Scholar 

  • Jacka, S.D. (1992): A martingale representation result and an application to incomplete financial markets. Math. Finance2, 239–250

    Google Scholar 

  • Kabanov, Yu.M., Kramkov, D.O. (1993): No arbitrage and equivalent martingale measures: An elementary proof of the Harrison-Pliska theorem. Moscow: Central Economics and Mathematics Institute. (Preprint)

    Google Scholar 

  • Karatzas, I., Lehoczky, J.P., Shreve, S.E., Xu, G.L. (1991): Martingale and duality methods for utility maximisation in an incomplete Market. SIAM J. Control Optimization29, 702–730

    Google Scholar 

  • Karatzas, I., Shreve, S.E. (1988): Brownian motion and stochastic calculus. Berlin Heidelberg New York: Springer

    Google Scholar 

  • Kreps, D. (1981): Arbitrage and equilibrium in economies with infinitely many commodities. J. Math. Econ.8, 15–35

    Google Scholar 

  • Kusuoka, S. (1993): A remark on arbitrage and martingale and martingale measures. Publ. Res. Inst. Math. Sci. (to appear)

  • Lakner, P. (1992): Martingale measures for right continuous processes which are bounded below. (Preprint)

  • Lépingle, D. (1978): Une inégalité de martingales. In: Dellacherie, C. et al. (eds.) Sémin. de Probab. XII. (Lect. Notes Math., vol. 649, pp. 134–137) Berlin Heidelberg New York: Springer

    Google Scholar 

  • Loève, M. (1978): Probability theory, 4th ed. Berlin Heidelberg New York: Springer

    Google Scholar 

  • Mc Beth, D.W. (1991): On the existence of equivalent martingale measures. Thesis Cornell University

  • Merton, R. (1973): The theory of rational option pricing. Bell J. Econ. Manag. Sci.4, 141–183

    Google Scholar 

  • Memin, J. (1980): Espaces de semi martingales et changement de probabilité. Z. W. Verw. Geb.52, 9–39

    Google Scholar 

  • Meyer, P.A. (1976): Un cours sur les intégrales stochastiques. In: Meyer, P.A. (ed.) Séminaire de Probabilité X. (Lect. Notes Math., vol. 511, pp. 245–400) Berlin Heidelberg New York: Springer

    Google Scholar 

  • Protter, Ph (1990): Stochastic integration and differential equations, a new approach. Berlin Heidelberg New York: Springer

    Google Scholar 

  • Revuz, D., Yor, M. (1991): Continuous martingales and Brownian motion. Berlin Heidelberg New York: Springer

    Google Scholar 

  • Rogers, C. (1993): Equivalent martingale measures and no-arbitrage. Queen Mary and Westfield College (Preprint)

  • Schachermayer, W. (1992): A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time. Insur. Math. Econ.11, 1–9

    Google Scholar 

  • Schachermayer, W. (1993): Martingale measures for discrete time processes with infinite horizon. Math. Finance, Vol 4, 1994, 25–56

    Google Scholar 

  • Schachermayer, W. (1993b). A counterexample to several problems in the theory of asset pricing. Math. Finance, Vol 3, 1993, 217–230

    Google Scholar 

  • Stein, E. (1970): Topics in harmonic analysis. (Ann. Math. Stud., vol. 63) Princeton: Princeton University Press

    Google Scholar 

  • Stricker, C. (1990): Arbitrage et lois de martingale. Ann. Inst. Henri Poincaré26, 451–460

    Google Scholar 

  • Yan, J.A. (1980): Caractérisation d'une classe d'ensembles convexes deL 1 ouH 1. In: Azéma, J., Yor, M. (eds.) Séminaire de Probabilité XIV. (Lect. Notes Math., vol. 784, pp. 220–222) Berlin Heidelberg New York: Springer

    Google Scholar 

  • Yor, M. (1978): Sous-espaces denses dansL 1 ouH 1 et représentation des martingales. In: Dellacherie, C. et al. (es.) Séminaire de Probabilité XII. (Lect. Notes Math., vol. 649, pp. 265–309) Berlin Heidelberg New York: Springer

    Google Scholar 

  • Yor, M. (1978b): Inegalités entre processus minces et applications. C.R. Acad. Sci., Paris, Ser. A286, 799–801

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Delbaen, F., Schachermayer, W. A general version of the fundamental theorem of asset pricing. Math. Ann. 300, 463–520 (1994). https://doi.org/10.1007/BF01450498

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01450498

Keywords

Navigation