Martingale measures and hedging for discrete-time financial markets

Mathematics of Operations Research

Volumn 24, Issue 2, 1999, Pages 509-528

  Schäl, Manfred ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FINANCE; MARKETING; MARKOV PROCESSES; MATHEMATICAL MODELS; SALES; VECTORS;

HEDGING OF OPTIONS; MARTINGALE MEASURES; OPTION PRICING; PORTFOLIO PLANS;

RANDOM PROCESSES;

EID: 0032677629     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.24.2.509     Document Type: Article

References (38)

1. Ansel, J. P., C. Stricker. 1990. Quelques remarques sur un théorèrne de Yan. Sem. de Probabilités. Lecture Notes in Mathematics XXIV. Springer, Berlin, Germany 266-274.
2. Artzner, P. 1997. On the numeraire portfolio. M. A. H. Dempster, S. R. Pliska, ed. Mathematics of Derivative Securities, Cambridge University Press, Cambridge, Massachusetts, 216-226.
3. Back, F., S. R. Pliska. 1990. On the fundamental theorem of asset pricing with an infinite state space. J. Math. Econ. 20 1-18.
4. Chow, Y. S., H. Robbins, D. Siegmund. 1971. Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, Boston.
5. Cvitanic, J., I. Karatzas. 1993. Hedging contingent claims with constrained portfolios. Ann. Appl. Probab. 3 652-681.
6. Dalang, R. C., A. Morton, W. Willinger. 1990. Equivalent martingale measures and no-arbitrage in stochastic securities market models. Stochastics Stochastic Rep. 29 185-201.
7. Davis, M. H. A. 1997. Option pricing in incomplete markets. M. A. H. Dempster, S. R. Pliska, ed. Mathematics of Derivative Securities, Cambridge University Press, Cambridge, Massachusetts, 216-226.
8. Delbaen, F., W. Schachermayer. 1994. Mathematical theory of arbitrage. Seminar notes, preliminary version.
9. Dubins, L. E., W. D. Sudderth. 1977. Countably additive gambling and optimal stopping. Z. Wahrscheinlichkeits-theorie verw. Gebiet 41 59-72.
10. E1 Karoui, N., M. Jeanblanc-Picqué. 1993. Robustness of the Black and Scholes formula. Working paper.
11. _, M. C. Quenez. 1995. Dynamic programming and pricing of contingent claims in an incomplete market. SIAM J. Control Optim. 33 29-66.
12. Fakeev, A. G. 1970. Optimal stopping rules for processes with continuous parameter. Theory Probab. Appl. 15 324-331.
13. Föllmer, H., Yu. M. Kabanov. 1998. Optional decomposition and Lagrange multipliers. Finance Stochast. 2 69-81.
14. _, D. Kramkov. 1997. Optional decompositions under constraints. Probab. Theory Relat. Fields 190 1-25.
15. _, M. Schweizer. 1989. Hedging by sequential regression: An introduction to the mathematics of option trading. The ASTIN Bulletin 1 147-160.
16. _, _. 1990. Hedging of contingent claims under incomplete information. M. H. A. Davis and R. J. Elliot, eds. Applied Stochastic Analysis. Gordon and Breach, London, UK.
17. Gerber, H. U., E. S. W. Shiu. 1994. Option pricing by Esscher transforms. Trans. Soc. Actuaries 46.
18. Harrison, J. M., D. M. Kreps. 1979. Martingales and arbitrage in multiperiod securities markets. J. Econom. Theory 20 381-408.
19. Hinderer, K. 1970. Foundations of nonstationary dynamic programming with discrete time-parameter. Lecture Notes in Operations Research and Mathematical Systems 33 Springer, Berlin-Heidelberg-New York.
20. Hordijk, A. 1974. Dynamic Programming and Markov potential theory. Mathematical Centre Tracts 51. Amsterdam, The Netherlands.
21. Jacod, J., A. N. Shiryaev. 1998. Local martingales and the fundamental asset pricing theorems in the discrete-time case. Finance Stochast. 3 259-273.
22. Karatzas, I. 1988. On the pricing of American options. Appl. Math. Optim. 17 37-60.
23. _, S. G. Kou. 1996. On the pricing of contingent claims under constraints. Ann. Appl. Probab. 6 321-369.
24. Kramkov, D. O. 1996. Optional decomposition of supermartingales and hedging of contingent claims in incomplete security markets. Probab. Theory Relat. Fields 105 459-479.
25. Levy, H., A. Levy. 1988. Option valuation: An extension of the binomial model. Conference HEC. Paris.
26. Long, J. 1990. The numeraire portfolio. J. Finance 44 205-209.
27. Merton, R. C. 1973. Theory of rational option pricing. Bell. J. Econom. Management. Sci. 4 141-183.
28. Naik, V., R. Uppal. 1992. Minimum cost hedging in incomplete markets. Univ. of British Columbia. Working paper.
29. Rogers, L. C. G. 1994. Equivalent martingale measures and no-arbitrage. Stochastics Stochastic Rep. 51 41-49.
30. Rubinstein, M. 1976. The valuation of uncertain income streams and the pricing of options. Bell J. Econom. Management Sci., 407-425.
31. Schachermayer, W. 1992. A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time. Insurance: Mathematics and Economics 11 249-257.
32. Schäl, M. 1971. Ein verallgemeinertes stationäres Entscheidungsmodell der dynamischen Optimierung. Vol. X, 145-162: Methods of Operations Research, ed. R. Henn. Meisenheim: Anton Hain.
33. _. 1974. A selection theorem for optimization problems. Arch. Math, xxv 219-224.
34. _. 1994. On quadratic cost criteria for option hedging. Math. Oper. Res. 19 121-131.
35. 2-closedness property for discrete-time financial markets. Working paper.
36. Schweizer, M. 1995. Variance-optimal hedging in discrete time. Math. Oper. Res. 20 1-32.
37. _. 1996. Approximation pricing and the variance-optimal martingale measure. Ann. Probab. 24 206-236.
38. Strauch, R. E. 1966. Negative dynamic programming. Ann. Math. Statist. 37 871-890.