Optimal stopping of Hunt and Lévy processes

References

• Bertoin , J. 1996 . Lévy Processes , Cambridge : Cambridge University Press .
   Google Scholar
• Blumenthal , R.M. and Getoor , R.K. 1968 . Markov Processes and Potential Theory , New York, London : Academic Press .
   Google Scholar
• Boyarchenko , S.I. and Levendorskij , S.Z. 2002 . Non-Gaussian Merton–Black–Scholes Theory , Singapore : World Scientific .
   Google Scholar
• Chan, T., 2000, Pricing perpetual American options driven by spectrally one-sided Lévy processes, Preprint.
   Google Scholar
• Darling , D.A. , Liggett , T. and Taylor , H.M. 1972 . Optimal stopping for partial sums . Annals of Mathematical Statistics , 43 : 1363 – 1368 .
   Google Scholar
• Dynkin , E.B. 1963 . The optimum choice of the instant for stopping a Markov process . Doklady Akademii Nauk SSSR , 150 ( 2 ) : 238 – 240 .
   Google Scholar
• Dynkin , E.B. 1969 . Prostranstvo vyhodov markovskogo processa . Uspehi Mat. Nauk (English translation in Russian Mathematical Survey) , XXIV 4 ( 148 ) : 89 – 152 .
   Google Scholar
• Folland , G.B. 1999 . Real Analysis , 2nd ed. , New York : Wiley .
   Google Scholar
• Gerber , H.U. and Shiu , E.S.W. 1998 . Pricing perpetual options for jump processes . North American Actuarial Journal , 2 ( 3 ) : 101 – 112 .
   Google Scholar
• Kou , S.G. and Wang , H.T. 2004 . Option pricing under a double exponential jump diffusion model . Management Science , 50 ( 9 ) : 1178 – 1192 .
   Web of Science ®Google Scholar
• Kunita , H. and Watanabe , T. 1965 . Markov processes and Martin boundaries. I . Illinois Journal of Mathematics , 9 ( 3 ) : 485 – 526 .
   Google Scholar
• Kyprianou , A.E. and Surya , B.A. 2005 . On the Novikov–Shiryaev optimal stopping problems in continuous time . Electronic Communications in Probability , 10 : 146 – 154 .
   Web of Science ®Google Scholar
• McKean , H.P. 1965 . A free boundary problem for the heat equation arising from a problem in mathematical economics . Industrial Management Review , 6 : 32 – 39 .
   Web of Science ®Google Scholar
• Mordecki , E. 1997 . Optimal stopping for a compound Poisson process with exponential jumps . Publicaciones Matemáticas del Uruguay , 7 : 55 – 66 .
   Google Scholar
• Mordecki , E. 2002 . Optimal stopping and perpetual options for Lévy processes . Finance and Stochastics , 6 ( 4 ) : 473 – 493 .
   Web of Science ®Google Scholar
• Mordecki , E. 2002 . “ Perpetual options for Lévy processes in the Bachelier model ” . In Proc. Steklov Inst. Math. Stochastic Financial Mathematics , Edited by: Shiryaev , A.N. Vol. 237 , 247 – 255 . Moscow : Nauka .
   Google Scholar
• Novikov , A. and Shiryaev , A. 2006 . “ On the solution of the optimal stopping problem for random walks and Lévy process ” . In Symposium on Optimal Stopping with Applications 22 – 27 . Manchester, UK, January
   Google Scholar
• Novikov , A. and Shiryaev , A.N. 2004 . On an effective solution of the optimal stopping problem for random walks . Theory of Probability and its Applications , 49 : 373 – 382 .
   Web of Science ®Google Scholar
• Rogozin , B.A. 1966 . On distributions of functionals related to boundary problems for processes with independent increments . Theory of Probability and its Applications , 11 : 580 – 591 .
   Web of Science ®Google Scholar
• Salminen , P. 1985 . Optimal stopping of one-dimensional diffusions . Mathematische Nachrichten , 124 : 85 – 101 .
   Web of Science ®Google Scholar
• Sato , K. 1999 . Lévy Processes and Infinitely Divisible Distributions , Cambridge : Cambridge Press .
   Google Scholar
• Shiryayev , A.N. 1978 . Optimal Stopping Rules , New York, Heidelberg, Berlin : Springer Verlag .
   Google Scholar
• Snell , L. 1953 . Applications of martingale system theorems . Transactions of the American Mathematical Society , 73 : 293 – 312 .
   Web of Science ®Google Scholar