On the American option problem

Mathematical Finance

Volumn 15, Issue 1, 2005, Pages 169-181

  Peskir, Goran ^a  

^a AARHUS UNIVERSITY   (Denmark)

Author keywords

American put option; Arbitrage free price; Curved boundary; Free boundary problem; Geometric Brownian motion; Local time space calculus; Nonlinear integral equation; Optimal stopping; Smooth fit

Indexed keywords

EID: 14544284499     PISSN: 09601627     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0960-1627.2005.00214.x     Document Type: Article

References (21)

1. BATHER, I (1970): Optimal Stopping Problems for Brownian Motion, Adv. Appl. Probab. 2, 259-286.
2. CARR, P., R. JARROW, and R. MYNENI (1992): Alternative Characterizations of American Put Options, Math. Finance 2, 78-106.
3. CHERNOFF, H. (1968): Optimal Stochastic Control. Sankhyā Ser. A 30, 221-252.
4. DYNKIN, E. B. (1963): The Optimum Choice of the Instant for Stopping a Markov Process, Soviet Math. Dokl 4, 627-629.
5. FRIEDMAN, A. (1959): Free Boundary Problems for Parabolic Equations. I. Melting of Solids, J. Math. Mech. 8, 499-518.
6. GRIGELIONIS, B. I., and A. N. SHIRYAEV (1966): On Stefan's Problem and Optimal Stopping Rules for Markov Processes, Theory Prob. Appl. 11, 541-558.
7. LITTLE T., V. PANT, and C., HOU (2000): A New Integral Representation of the Early Exercise Boundary for American Put Options, J. Computat. Finance 3, 73-96.
8. JACKA, S. D. (1991): Optimal Stopping and the American Put, Math. Finance 1, 1-14.
9. JACKA, S. D. (1993): Local Times, Optimal Stopping and Semimartingales, Ann. Prob. 21, 329-339.
10. KARATZAS, I., and S. E. SHREVE (1998): Methods of Mathematical Finance. New York: Springer-Verlag.
11. KIM, I. J. (1990): The Analytic Valuation of American Options, Rev. Financial Stud. 3, 547-572.
12. KOLODNER, I. I. (1956): Free Boundary Problem for the Heat Equation with Applications to Problems of Change of Phase. I. General Method of Solution, Comm. Pure Appl. Math. 9, 1-31.
13. McKEAN, H. P., Jr. (1965): Appendix: A Free Boundary Problem for the Heat Equation Arising from a Problem of Mathematical Economics, Ind. Mgmt. Rev. 6, 32-39.
14. MIRANKER, W. L. (1958): A Free Boundary Value Problem for the Heat Equation, Quart. Appl. Math. 16, 121-130.
15. MYNENI, R. (1992): The Pricing of the American Option, Ann. Appl. Probab. 2, 1-23.
16. PESKIR, G. (2002b): On Integral Equations Arising in the First-Passage Problem for Brownian Motion. J. Integral Equations Appl. 14, 397-423.
17. PESKIR, G. (2002a): A Change-of-Variable Formula with Local Time on Curves. To appear in J. Theoret. Probab.
18. PESKIR, G. (2003): The Russian Option: Finite Horizon. To appear in Finance Stoch.
19. SNELL, J. L. (1952): Applications of Martingale System Theorems, Trans. Amer. Math. Soc. 73, 293-312.
20. TRICOMI, F. G. (1957): Integral Equations. New York: Interscience Publishers.
21. VAN MOERBEKE, P. (1976): On Optimal Stopping and Free Boundary Problems, Arch. Rational Mech. Anal. 60, 101-148.