Pricing derivatives of American and game type in incomplete markets

Finance and Stochastics

Volumn 8, Issue 2, 2004, Pages 261-284

  Kallsen, Jan ^a   Kühn, Christoph ^b  

^a UNIVERSITY OF FREIBURG   (Germany)

^b GOETHE UNIVERSITY   (Germany)

Author keywords

supermartingales; American options; Dynkin game; Game contingent claims; Incomplete markets; Neutral derivative pricing

Indexed keywords

EID: 24144460915     PISSN: 09492984     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00780-003-0110-7     Document Type: Article

References (43)

1. Barndorff-Nielsen, O.: Processes of normal inverse Gaussian type. Finance Stochast. 2, 41-68 (1998)
2. Bensoussan, A.: On the theory of option pricing. Acta Appl. Math. 2, 139-158 (1984)
3. Cherny, A., Shiryaev, A.: Vector stochastic integrals and the fundamental theorems of asset pricing. Preprint 2001
4. Cvitanić, J., Karatzas, I.: Backward stochastic differential equations with reflection and Dynkin games. Ann. Probab. 24, 2024-2056 (1996)
5. Cvitanić, J., Pham, H., Touzi, N.: Super-replication in stochastic volatility models under portfolio constraints. J. Appl. Probab. 36, 523-545 (1999)
6. Davis, M., Zariphopoulou, T.: American options and transaction fees. In: Davis, M. (ed.) Mathematical finance, vol. 65 of (The IMA Volumes in Mathematics and Its Applications). Berlin Heidelberg New York: Springer 1995, pp. 47-61
7. Delbaen, F., Schachermayer, W.: A general version of the fundamental theorem of asset pricing. Math. Ann. 300, 463-520 (1994)
8. Delbaen, F., Schachermayer, W.: The fundamental theorem of asset pricing for unbounded stochastic processes. Math. Ann. 312, 215-250 (1998)
9. Dellacherie, C., Meyer, P.: Probabilities and potential B. Amsterdam: North-Holland 1982
10. Eberlein, E., Jacod, J.: On the range of option prices. Finance Stochast. 1, 131-140 (1997)
11. Eberlein, E., Keller, U.: Hyperbolic distributions in finance. Bernoulli 1, 281-299 (1995)
12. Eberlein, E., Keller, U., Prause, K.: New insights into smile, mispricing and value at risk: The hyperbolic model. J. Bus. 71, 371-406 (1998)
13. Emery, M.: Stabilité des solutions des équations différentielles stochastiques. Application aux intégrales multiplicatives stochastiques. Z. Wahrsch, Verw. Geb. 41, 241-262 (1978)
14. Föllmer, H., Kabanov, Y.: Optional decomposition and Lagrange multipliers. Finance Stochast. 2, 69-81 (1998)
15. Föllmer, H., Kramkov, D.: Optional decompositions under constraints. Probab. Theory Rel. Fields 109, 1-25 (1997)
16. Föllmer, H., Schweizer, M.: Hedging of contingent claims under incomplete information. In: Davis, M.H.A., Elliott, R.J. (eds.) Applied Stochastic Analysis, vol. 5 of Stochastics Monographs. London: Gordon & Breach 1991, pp. 389-414
17. Frey, R., Sin, C.: Bounds on European option prices under stochastic volatility. Math. Finance 9(2), 97-116 (1999)
18. Goll, T., Kallsen, J.: A complete explicit solution to the log-optimal portfolio problem. Ann. Appl. Probab. 13, 774-799 (2003)
19. Hugonnier, J., Kramkov, D., Schachermayer, W.: On the utility based pricing of contingent claims in incomplete markets. Preprint 2003
20. Jacod, J.: Calcul Stochastique et Problèmes de Martingales, Vol. 714 (Lecture Notes in Mathematics). Berlin Heidelberg New York: Springer 1979
21. Jacod, J., Shiryaev, A.: Limit theorems for stochastic processes, 2nd ed. Berlin Heidelberg New York: Springer 2003
22. Kabanov, Y.: On the FTAP of Kreps-Delbaen-Schachermayer. In: Statistics and control of stochastic processes (Moscow, 1995/1996). River Edge, NJ: World Scientific 1997, pp. 191-203
23. Kallsen, J.: A utility maximization approach to hedging in incomplete markets. Math. Meth. Oper. Res. 50, 321-338 (1999)
24. Kallsen, J.: Optimal portfolios for exponential Lévy processes. Math. Meth. Oper. Res. 51, 357-374 (2000)
25. Kallsen, J.: Derivative pricing based on local utility maximization. Finance Stochast. 6, 115-140 (2002a)
26. Kallsen, J.: Utility-based derivative pricing in incomplete markets. In: Geman, H., Madan, D., Pliska, S., Vorst, T. (eds.) Mathematical finance - Bachelier Congress 2000. Berlin Heidelberg New York: Springer 2002b, pp. 313-338.
27. Kallsen, J.: σ-localization and σ-martingales. Theory Probab. Its Appl. (forthcoming) (2003)
28. Kallsen, J., Shiryaev, A.: Time change representations of stochastic integrals. Theory Probab. Its Appl. 46, 522-528 (2002)
29. Karatzas, I.: On the pricing of American options. Appl. Math. Optimization 17, 37-60 (1988)
30. Karatzas, I., Kou, S.: Hedging American contingent claims with constrained portfolios. Finance Stochast. 3, 215-258 (1998)
31. Kifer, Y.: Game options. Finance Stochast. 4, 443-463 (2000)
32. Kramkov, D.: Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets. Probab. Theory Rel. Fields 105, 459-479 (1996)
33. Kramkov, D., Schachermayer, W.: The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 9, 904-950 (1999)
34. Kühn, C.: Game contingent claims in complete and incomplete markets. Preprint 2001
35. Kühn, C.: Pricing contingent claims in incomplete markets when the holder can choose among different payoffs. Ins. Math. Econ. 31, 215-233 (2002)
36. Kyprianou, A.: Some calculations for Israeli options. Finance Stochast. (forthcoming) (2003)
37. Lepeltier, J., Maingueneau, M.: Le jeu de Dynkin en théorie générale sans l'hypothèse de Mokobodski. Stochast. 13, 25-44 (1984)
38. Madan, D., Seneta, E.: The VG model for share market returns. J. Bus. 63, 511-524 (1990)
39. Protter, P.: On the existence, uniqueness, convergence and explosions of solutions of systems of stochastic integral equations. Ann. Probab. 5, 243-261 (1977)
40. Protter, P.: HP stability of solutions of stochastic differential equations. Z. Wahrsch. Verw. Geb. 44, 337-352 (1978)
41. Protter, P.: Stochastic integration and differential equations, 2nd ed. Berlin Heidelberg New York: Springer 1992
42. Rockafellar, T., Wets, R.: Variational analysis. Berlin Heidelberg New York: Springer 1998
43. Schachermayer, W.: Optimal investment in incomplete financial markets. In: Geman, H., Madan, D., Pliska, S., Vorst, T. (eds.) Mathematical finance - Bachelier Congress 2000. Berlin Heidelberg New York: Springer 2002, pp. 427-462