A new look at optimal stopping problems related to mathematical finance

Statistica Sinica

Volumn 7, Issue 1, 1997, Pages 93-108

  Beibel, M ^a   Lerche, H R ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Generalized parking problems; Martingales; Optimal stopping; Perpetual options

Indexed keywords

EID: 0031508322     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. Beibel, M. (1996). A note on Ritov's Bayes approach to the minimax property of the cusum procedure. To appear in Ann. Statist.
2. n/n. Illinois J. Math. 9, 444-454.
3. Chow, Y. S., Robbins, H. and Siegmund, D. (1971). Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin Company, Boston.
4. Dvoretzky, A. (1965). Existence and properties of certain optimal stopping rules. 5th Berkeley Symp. I, 441-452.
5. Jacka, S. D. (1991). Optimal stopping and the American put. Math. Finance 2, 1-14.
6. Karatzas, I. (1988). On the pricing of American options. Appl. Math. Optim. 17, 37-60.
7. Lerche, H. R. (1986). Boundary Crossing of Brownian Motion. Lecture Notes in Statistics. Springer-Verlag, Berlin.
8. McKean, H. P. (1965). A free boundary problem for the heat equation arising from a problem in mathematical economics. Indust. Managment Review 6, 32-39.
9. Novikov, A. (1971). On stopping times for a Wiener process. Theory Probab. Appl. 16, 449-456.
10. Protter, P. (1990). Stochastic Integration and Differential Equations. Springer-Verlag, Berlin.
11. Samuelson, P. A. (1965). Rational theory of warrant pricing. Indust. Managment Review 6, 13-31.
12. Shepp, L. A. (1967). A first passage time problem for the Wiener process. Ann. Math. Statist. 38, 1912-1914.
13. Shepp, L. A. (1969). Explicit solutions to some problems of optimal stopping. Ann. Math. Statist. 40, 993-1010.
14. Shepp, L. A. and Shiryaev, A. N. (1993). The Russian option: reduced regret. Ann. Appl. Probab. 3, 631-640.
15. Shiryaev, A. N. (1963) On optimum methods in quickest detection problems. Theory Probab. Appl. 8, 22-46.
16. Taylor, H. M. (1968). Optimal stopping in a Markov process. Ann. Math. Statist. 39, 1333-1344.
17. van Moerbeke, P. (1974a). On optimal stopping and free boundary problems. Arch. Rational Mech. Anal. 60, 101-148.
18. van Moerbeke, P. (1974b). Optimal stopping and free boundary problems. Rocky Mountain J. Math. 4, 539-578.
19. Woodroofe, M., Lerche, R. and Keener, R. (1993). A generalized parking problem. In Statistical Decision Theory and related Topics V, p. 523-532. Springer-Verlag, Berlin.