No arbitrage under transaction costs, with fractional brownian motion and beyond

Mathematical Finance

Volumn 16, Issue 3, 2006, Pages 569-582

  Guasoni, Paolo ^a,b  

^a BOSTON UNIVERSITY   (United States)

^b USA   (United States)

Author keywords

Arbitrage; Fractional Brownian motion; Markov processes; Transaction costs

Indexed keywords

EID: 33745022624     PISSN: 09601627     EISSN: 14679965     Source Type: Journal    
DOI: 10.1111/j.1467-9965.2006.00283.x     Document Type: Article

References (34)

1. BARTON, R. J., and H. V. POOR (1988): Signal Detection in Fractional Gaussian Noise, IEEE Trans. Inform. Theory 34(5, part 1), 943-959.
2. BJÖRK, T., and H. HULT (2005): A Note on Wick Products and the Fractional Black-Scholes Model, Finance Stoch. 9(2), 197-209.
3. BOULEAU, N., and F. HIRSCH (1991): Dirichlet Forms and Analysis on Wiener Space, Vol. 14 of de Gruyter Studies in Mathematics. Berlin: Walter de Gruyter & Co.
4. CHERIDITO, P. (2003): Arbitrage in Fractional Brownian Motion Models, Finance Stoch. 7(4), 533-553.
5. CUTLAND, N. J., P. E. KOPP, and W. WILLINGER (1995): Stock Price Returns and the Joseph Effect: A Fractional Version of the Black-Scholes Model, in Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1993), Vol. 36 of Progr. Probab. Basel: Birkhäuser, 327-351.
6. DASGUPTA, A., and G. KALLIANPUR (2000): Arbitrage Opportunities for a Class of Gladyshev Processes, Appl. Math. Optim. 41(3), 377-385.
7. DECREUSEFOND, L. (2003): Stochastic Integration with Respect to Fractional Brownian Motion, in Theory and Applications of Long-Range Dependence. Boston: Birkhäuser, 203-226.
8. DECREUSEFOND, L., and A. S. ÜSTÜNEL (1999): Stochastic Analysis of the Fractional Brownian Motion, Potential Anal. 10(2), 177-214.
9. DELBAEN, F., and W. SCHACHERMAYER (1994): A General Version of the Fundamental Theorem of Asset Pricing, Math. Ann. 300(3), 463-520.
10. DELBAEN, F., and W. SCHACHERMAYER (1995): The Existence of Absolutely Continuous Local Martingale Measures, Ann. Appl. Probab. 5(4), 926-945.
11. DELLACHERIE, C., and P.-A. MEYER (1982): Probabilities and Potential. B, Vol. 72 of North-Holland Mathematics Studies, Theory of Martingales, translated from the French by J. P. Wilson. Amsterdam: North-Holland Publishing Co.
12. FÖLLMER, H., and A. SCHIED (2002): Stochastic Finance, Vol. 27 of de Gruyter Studies in Mathematics. Berlin: Walter de Gruyter & Co. (An introduction in discrete time.)
13. GRENANDER, U. (1981): Abstract Inference, Wiley Series in Probability and Mathematical Statistics. New York: John Wiley & Sons Inc.
14. GUASONI, P. (2002): Optimal Investment with Transaction Costs and without Semimartingales, Ann. Appl. Probab. 12(4), 1227-1246.
15. KABANOV, Y., M. RÁSONYI, and C. STRICKER (2002): No-Arbitrage Criteria for Financial Markets with Efficient Friction, Finance Stoch. 6(3), 371-382.
16. 0 and the Robust No-Arbitrage Property, Finance Stoch. 7(3), 403-411.
17. KABANOV, Y. M., and C. STRICKER (2001): The Harrison-Pliska Arbitrage Pricing Theorem under Transaction Costs, J. Math. Econ. 35(2), 185-196.
18. KALLIANPUR, G. (1971): Abstract Wiener Processes and Their Reproducing Kernel Hilbert Spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 17, 113-123.
19. KARATZAS, I., and S. E. SHREVE (1991): Brownian Motion and Stochastic Calculus, Vol. 113 of Graduate Texts in Mathematics, 2nd edn. New York: Springer-Verlag.
20. KARATZAS, I., and S. E. SHREVE (1998): Methods of Mathematical Finance, Vol. 39 of Applications of Mathematics (New York). New York: Springer-Verlag.
21. LI, W. V., and Q.-M. SHAO (2001): Gaussian Processes: Inequalities, Small Ball Probabilities and Applications, in Stochastic Processes: Theory and Methods, Vol. 19 of Handbook of Statist. Amsterdam: North-Holland, 533-597.
22. LIPTSER, R. S., and A. N. SHIRYAYEV (1989): Theory of Martingales, Vol. 49 of Mathematics and Its Applications (Soviet Series). Translated from the Russian by K. Dzjaparidze [Kacha Dzhaparidze], Dordrecht: Kluwer Academic Publishers Group.
23. MAHESWARAN, S., and C. A. SIMS (1993): Empirical Implications of Arbitrage-Free Asset Markets, in Models, Methods, and Applications of Econometrics: Essays in Honor of A. R. Bergstrom, P. Phillips, ed. Cambridge: Basil Blackwell, 301-316.
24. NORROS, I., E. VALKEILA, and J. VIRTAMO (1999): An Elementary Approach to a Girsanov Formula and Other Analytical Results on Fractional Brownian Motions, Bernoulli 5(4), 571-587.
25. PIPIRAS, V., and M. S. TAQQU (2000): Integration Questions Related to Fractional Brownian Motion, Probab. Theory Related Fields 118(2), 251-291.
26. REVUZ, D., and M. YOR (1994): Continuous Martingales and Brownian Motion, Vol. 293 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 2nd edn. Berlin: Springer-Verlag.
27. ROGERS, L. C. G. (1997): Arbitrage with Fractional Brownian Motion, Math. Finance 7(1), 95-105.
28. ROGERS, L. C. G., and D. WILLIAMS (2000): Diffusions, Markov Processes, and Martingales, Vol. 2. Cambridge Mathematical Library, Itô Calculus, Reprint, 2nd edn. (1994). Cambridge: Cambridge University Press.
29. SALOPEK, D. M. (1998): Tolerance to Arbitrage, Stochastic Process. Appl. 76(2), 217-230.
30. SAMKO, S. G., A. A. KILBAS, and O. I. MARICHEV (1993): Fractional Integrals and Derivatives, Theory and Applications, Edited and with a foreword by S. M. Nikol'skiǐ, translated from the 1987 Russian original, revised by the authors. Yverdon: Gordon and Breach Science Publishers.
31. SCHACHERMAYER, W. (2004): The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time, Math. Finance 14(1), 19-48.
32. SHIRYAEV, A. N. (1998): On Arbitrage and Replication for Fractal Models, Technical report, MaPhySto.
33. SOTTINEN, T. (2001): Fractional Brownian Motion, Random Walks and Binary Market Models, Finance Stoch. 5(3), 343-355.
34. WILLINGER, W., M. S. TAQQU, and V. TEVEROVSKY (1999): Stock Market Prices and Long-Range Dependence, Finance Stoch. 3(1), 1-13.