The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time

Mathematical Finance

Volumn 14, Issue 1, 2004, Pages 19-48

  Schachermayer, Walter ^a,b  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Arbitrage; Foreign exchange markets; Fundamental theorem of asset pricing; Proportional transaction costs

Indexed keywords

EID: 1042267699     PISSN: 09601627     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0960-1627.2004.00180.x     Document Type: Article

References (43)

1. ANSEL, J. P., and C. STRICKER (1994): Couverture des Actifs Contingents et Prix Maximum, Ann. Inst. H. Poincaré 30, 303-315.
2. BOUCHARD, B., YU. M. KABANOV, and N. TOUZI (2001): Option Pricing by Large Risk Aversion Utility under Transaction Costs, Decisions Econ. & Finance 24(1), 127-136.
3. BOUCHARD, B., and N. TOUZI (2000): Explicit Solution of the Multivariate Superreplication Problem under Transaction Costs, Annals Appl. Prob. 10, 685-708.
4. CVITANIC, J., and I. KARATZAS (1996): Hedging and Portfolio Optimization under Transaction Costs: A Martingale Approach, Math. Finance 6(2), 133-165.
5. CVITANIC, J., H. PHAM, and N. Touzi (1999): A Closed-Form Solution to the Problem of Super-replication under Transaction Costs, Finance Stoch. 3, 35-54.
6. DALANG, R. C., A. MORTON, and W. WILLINGER (1990): Equivalent Martingale Measures and No-Arbitrage in Stochastic, Stoch. Stoch. Rep. 29, 185-201.
7. DAVIS, M. H. A., and A. NORMAN (1990): Portfolio Selection with Transaction Costs, Math. Oper. Res. 15, 676-713.
8. DELBAEN, F. (1992): Representing Martingale Measures When Asset Prices are Continuous and Bounded, Math. Finance 2, 107-130.
9. DELBAEN, F., YU. M. KABANOV, and E. VALKEILA (2002): Hedging under Transaction Costs in Currency Markets: A Discrete-Time Model, Math. Finance 12(1), 45-61.
10. DELBAEN, F., and W. SCHACHERMAYER (1994): A General Version of the Fundamental Theorem of Asset Pricing, Math. Annalen 300, 463-520.
11. DELBAEN, F., and W. SCHACHERMAYER (1998): The Fundamental Theorem of Asset Pricing for Unbounded Stochastic Processes, Math. Annalen 312, 215-250.
12. DUFFIE, D., and C. F. HUANG (1986): Multiperiod Security Markets with Differential Information; Martingales and Resolution Times, J. Math. Econ. 15, 283-303.
13. EVSTTGNEEV, I., and M. TAKSAR (2000): A general Framework for Arbitrage Pricing and Hedging Theorems in Models of Financial Markets. Preprint.
14. FLESAKER, B., and L. P. HUGHSTON (1997): International Models for Interest Rates and Foreign Exchange, Net Exposure 3, 55-79.
15. HARRISON, J. M., and D. M. KREPS (1979): Martingales and Arbitrage in Multiperiod Securities Markets, J. Econ. Theory 20, 381-408.
16. HARRISON, J. M., and S. R. PLISKA (1981): Martingales and Stochastic Integrals in the Theory of Continuous Trading, Stoch. Process. Appl. 11, 215-260.
17. JACKA, S. D. (1992): A Martingale Representation Result and an Application to Incomplete Financial Markets, Math. Finance 2, 239-250.
18. JOUINI, E., and H. KALLAL (1995a): Arbitrage in Securities Markets with Short-Sales Constraints, Math. Finance 3, 237-248.
19. JOUINI, E., and H. KALLAL (1995b): Martingales and Arbitrage in Securities Markets with Transaction Costs, J. Econ. Theory 66, 178-197.
20. JOUINI, E., and H. KALLAL (1999): Viability and Equilibrium in Securities Markets with Frictions, Math. Finance 9(3), 275-292.
21. KABANOV, YU. M. (1999): Hedging and Liquidation under Transaction Costs in Currency Markets, Finance Stoch. 3(2), 237-248.
22. KABANOV, YU. M. (2001): Arbitrage Theory; in Handbooks in Mathematical Finance. Option Pricing, Interest Rates and Risk Management (Eds. E. Jouini, J. Cvitanic, M. Musiela), Cambridge University Press, Cambridge, pp. 3-42.
23. KABANOV, YU. M., and D. KRAMKOV (1994): No Arbitrage and Equivalent Martingale Measures: An Elementary Proof of the Harrison-Pliska Theorem, Theory Prob. Appl. 39.
24. KABANOV, YU. M., and G. LAST (2002): Hedging under Transaction Costs in Currency Markets: A Continuous-Time Model, Math. Finance 12(1), 63-70.
25. KABANOV, YU. M., and CH. STRICKER (2001a): The Harrison-Pliska Arbitrage Pricing Theorem under Transaction Costs, J. Math. Econ. 35(2), 185-196.
26. KABANOV, YU. M., and CH. STRICKER (2001b): A Teachers' Note on No-Arbitrage Criteria, Lect. Notes Math. 1755, 149-152.
27. KABANOV, YU. M., M. RÁSONYI, and CH. STRICKER (2002): No-Arbitrage Criteria for Financial Markets with Efficient Friction, Fin. and Stoch. 6(3), 371-382.
28. 0 and the Robust No-Arbitrage Property, Fin. and Stoch. 7(3), 403-411.
29. KOEHL, P.-F., H. PHAM, and N. Touzi (1999): On Super-replication under Transaction Costs in General Discrete-Time Models, Theory Prob. Appl. 45, 783-788.
30. KREPS, D. M. (1981): Arbitrage and Equilibrium in Economies with Infinitely Many Commodities, J. Math. Econ. 8, 15-35.
31. LEROY, S. F., and J. WERNER (2001): Principles of Financial Economics. Cambridge: Cambridge University Press.
32. LEVENTAL, S., and A. V. SKOROHOD (1997): On the Possibility of Hedging Options in the Presence of Transaction Costs, Ann. Appl. Prob. 7, 410-443.
33. PENNER, I. (2001): Arbitragefreiheit in Finanzmärkten mit Transaktionskosten. Diploma thesis, Humboldt University Berlin.
34. PHAM, H., and N. Touzi (1999): The Fundamental Theorem of Asset Pricing with Cone Constraints, J. Math. Econ. 31, 265-279.
35. ROGERS, L. C. G. (1994): Equivalent Martingale Measures and No-Arbitrage, Stock. Stoch. Rep. 51, 41-49.
36. SCHACHERMAYER, W. (1992): A Hilbert Space Proof of the Fundamental Theorem of Asset Pricing in Finite Discrete Time, Insurance: Math. & Econ. 11, 249-257.
37. SCHACHERMAYER, W. (1994): Martingale Measures for Discrete Time Processes with Infinite Horizon, Math. Finance 4(1), 25-55.
38. SCHACHERMAYER, W. (2003): Introduction to the Mathematics of Financial Markets; in Lecture Notes in Mathematics 1816: Lectures on Probability Theory and Statistics (Ed. P. Bernard), Springer Verlag, Berline, pp. 111-177.
39. SONER, H. M., S. E. SHREVE, and J. CVITANIC (1995): There Is No Nontrivial Hedging Portfolio for Option Pricing with Transaction Costs, Ann. Appl. Prob. 5, 327-355.
40. STRASSER, H. (1997): On a Lemma of Schachermayer. Preprint, Vienna University of Economics and Business Administration (9 pages).
41. STRICKER, C. (1990): Arbitrage et Lois de Martingale, Ann. Inst. H. Poincaré Probab. Statist. 26, 451-460.
42. TOUZI, N. (1999): Super-replication under Proportional Transaction Costs: From Discrete to Continuous-Time Models, Math. Methods Oper. Res. 50, 297-320.
43. 1, Lect. Notes Math. 784, 220-222.