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A note on pasting conditions for the American perpetual optimal stopping problem

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  • Christensen, Sören
  • Irle, Albrecht

Abstract

The principles of smooth and continuous pasting play an important role in the study of optimal stopping problems with jump processes. These principles state that the optimal stopping boundary is selected so that the value function is smooth and continuous, respectively (depending on the behavior of the underlying process at the boundary). Extending the results of Alili & Kyprianou [Alili, L., Kyprianou, A.E., 2005. Some remarks on first passage of Lévy processes, the American put and pasting principles. Ann. Appl. Probab. 15, 2062-2080] we show that in the case of an American perpetual put under a Lévy process the optimal stopping point is in fact characterized as the only point that fulfills this smooth/continuous pasting condition.

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  • Christensen, Sören & Irle, Albrecht, 2009. "A note on pasting conditions for the American perpetual optimal stopping problem," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 349-353, February.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:3:p:349-353
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    References listed on IDEAS

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    1. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    2. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
    3. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
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    1. Christensen, Sören & Salminen, Paavo & Ta, Bao Quoc, 2013. "Optimal stopping of strong Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1138-1159.
    2. Soren Christensen, 2011. "A method for pricing American options using semi-infinite linear programming," Papers 1103.4483, arXiv.org, revised Jun 2011.

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