An effective method for the explicit solution of sequential problems on the real line

References

• Alili, L. and Kyprianou, A. E. (2005). Some Remarks on First Passage of Lévy Processes, the American Put and Pasting Principles, Annals of Applied Probability 15: 2062–2080.
   Web of Science ®Google Scholar
• Alvarez, L. and Matomäki, P. (2015). Expected Supremum Representation and Optimal Stopping, ArXiv e-prints 1505.01660.
   Google Scholar
• Asmussen, S., Avram, F., and Pistorius, M. (2004). Russian and American Put Options under Exponential Phase-Type Lévy Models, Stochastic Processes and Their Applications 109: 79–111.
   Web of Science ®Google Scholar
• Aven, T. and Jensen, U. (2013). Stochastic Models in Reliability, New York: Springer.
   Google Scholar
• Beibel, M. (1998). Generalized Parking Problems for Lévy Processes, Sequential Analysis 17: 151–171.
   Google Scholar
• Blumenthal, R. M. and Getoor, R. K. (1968). Markov Processes and Potential Theory, New York: Academic Press.
   Google Scholar
• Boguslavskaya, E. (2014). A Method to Solve Optimal Stopping Problems for Lévy Processes in Infinite Horizon, ArXiv e-prints 1403.1816.
   Google Scholar
• Borodin, A. and Salminen, P. (2002). Handbook on Brownian Motion—Facts and Formulæ, Basel: Birkhäuser.
   Google Scholar
• Boyarchenko, S. and Levendorski, S. (2007). Irreversible Decisions under Uncertainty, Berlin: Springer.
   Google Scholar
• Chow, Y. S., Robbins, H., and Siegmund, D. (1971). Great Expectations: The Theory of Optimal Stopping, Boston: Houghton Mifflin.
   Google Scholar
• Christensen, S. and Irle, A. (2009). A Note on Pasting Conditions for the American Perpetual Optimal Stopping Problem, Statistics & Probability Letters 79: 349–353.
   Web of Science ®Google Scholar
• Christensen, S., Irle, A., and Novikov, A. (2011). An Elementary Approach to Optimal Stopping Problems for AR(1) Sequences, Sequential Analysis 30: 79–93.
   Web of Science ®Google Scholar
• Christensen, S. and Salminen, P. (2015). Impulse Control and Expected Suprema, Advances in Applied Probability, in press.
   Google Scholar
• Christensen, S., Salminen, P., and Ta, B. Q. (2013). Optimal Stopping of Strong Markov Processes, Stochastic Processes and Their Applications 123: 1138–1159.
   Web of Science ®Google Scholar
• Chung, K. L. and Walsh, J. B. (2005). Markov Processes, Brownian Motion, and Time Symmetry, New York: Springer.
   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
• Deligiannidis, G., Le, H., and Utev, S. (2009). Optimal Stopping for Processes with Independent Increments, and Applications, Journal of Applied Probability 46: 1130–1145.
   Web of Science ®Google Scholar
• Föllmer, H. and Knispel, T. (2006). A Representation of Excessive Functions as Expected Suprema, Probability and Mathematical Statistics 26: 379–394.
   Google Scholar
• Irle, A. (1979). Monotone Stopping Problems and Continuous Time Processes, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 48: 49–56.
   Web of Science ®Google Scholar
• Irle, A. (1981). Locally Most Powerful Sequential Tests for Stochastic Processes, Stochastic Processes and Their Applications 11: 285–291.
   Google Scholar
• Irle, A. (1982). On the Infinitesimal Characterization of Monotone Stopping Problems in Continuous Time, Lecture Notes in Statistics: Mathematical Learning Models—Theory and Algorithms (Bad Honnef, 1982) 20: 93–100.
   Google Scholar
• Jensen, U. (1989). Monotone Stopping Rules for Stochastic Processes in a Semimartingale Representation with Applications, Optimization 20: 837–852.
   Google Scholar
• Kyprianou, A. E. (2006). Introductory Lectures on Fluctuations of Lévy Processes with Applications, Berlin: Springer.
   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
• Lorden, G. (1977). Nearly-Optimal Sequential Tests for Finitely Many Parameter Values, Annals of Probability 5: 1–21.
   Google Scholar
• Millar, P. W. (1978). A Path Decomposition for Markov Processes, Annals of Probability 6: 345–348.
   Web of Science ®Google Scholar
• Mordecki, E. (2002). Optimal Stopping and Perpetual Options for Lévy Processes, Finance and Stochastics 6: 473–493.
   Web of Science ®Google Scholar
• Mordecki, E. and Salminen, S. (2007). Optimal Stopping of Hunt and Lévy Processes, Stochastics 79: 233–251.
   Google Scholar
• Morton, A. J. and Pliska, S. (1995). Optimal Portfolio Management with Fixed Transaction Costs, Mathematical Finance 5: 337–356.
   Google Scholar
• Novikov, A. and Shiryaev, A. (2004). On an Effective Case of the Solution of the Optimal Stopping Problem for Random Walks, Teoriya Veroyatnostei i ee Primeneniya 49: 373–382.
   Web of Science ®Google Scholar
• Novikov, A. and Shiryaev, A. (2007). On Solution of the Optimal Stopping Problem for Processes with Independent Increments, Stochastics 79: 393–406.
   Google Scholar
• Paulsen, V. (2000). On Optimal Stopping of One-Dimensional Symmetric Diffusions with Nonlinear Costs of Observations, Habilitation Treatise, University of Kiel.
   Google Scholar
• Salminen, P. (2011). Optimal Stopping, Appell Polynomials, and Wiener-Hopf Factorization, Stochastics 83: 611–622.
   Google Scholar
• Sharpe, M. (1988). General Theory of Markov Processes, Boston: Academic Press.
   Google Scholar
• Shiryaev, A. (1978). Optimal Stopping Rules, New York: Springer.
   Google Scholar
• Surya, B. A. (2007). An Approach for Solving Perpetual Optimal Stopping Problems Driven by Lévy Processes, Stochastics 79: 337–361.
   Google Scholar
• Woodroofe, M., Lerche, R., and Keener, R. (1994). A Generalized Parking Problem, in Statistical Decision Theory and Related Topics V, S. Gupta and J. Berger, eds., pp. 523–532, New York: Springer.
   Google Scholar