![]() Thus, optimal stopping rules in the constrained case qualitatively differ from optimal rules in the unconstrained case. In contrast to the unconstrained case, optimal stopping rules, in general, cannot be found among interval exit times. Stopping at the intermediate point means that the testing is abandoned without accepting H 0 or H 1. We impose an expectation constraint on the stopping rules allowed and show that an optimal stopping rule satisfying the constraint can be found among the rules of the following type: stop if the posterior probability for H 1 attains a given lower or upper barrier or stop if the posterior probability comes back to a fixed intermediate point after a sufficiently large excursion. ** Corresponding author: study a stopping problem arising from a sequential testing of two simple hypotheses H 0 and H 1 on the drift rate of a Brownian motion. TU Wien, Institute of Statistics and Mathematical Methods in Economics, 3-4, 337-361.Institute for Mathematics, University of Jena, An approach for solving perpetual optimal stopping problems driven by Lévy processes. Springer-Verlag, New York-Heidelberg, 1978. Stochastic Modelling and Applied Probability. Applications of Mathematics (New York), 21. Stochastic integration and differential equations. Séminaire de Probabilités XXXVIII, 30-41, Lecture Notes in Math., 1857, Springer, Berlin, 2005. A potential-theoretical review of some exit problems of spectrally negative Lévy processes. Optimal stopping and free-boundary problems. Advances in finance and stochastics, 295-312, Springer, Berlin, 2002. Sequential testing problems for Poisson processes. Optimal stopping and perpetual options for Lévy processes. Zero-one laws and the minimum of a Markov process. Heat equation arising from a problem of mathematical economics. Appendix: A free boundary problem for the Smoothness and convexity of scale functions withĪpplications to de Finetti's control problem. As usual in this framework, the initial optimal stopping. Kyprianou, Andreas E., Rivero, Victor Song, Renming. We present the sequential testing of two simple hypotheses for a large class of Lvy processes.Séminaire de Probabilités XL 97-105, Lecture Notes in Math., 1899, Springer, Berlin, 2007. A note on a change of variable formula with local time-space for Lévy processes of Introductory lectures on fluctuations of Lévy processes with applications. Perpetual convertible bonds in jump-diffusion models. Problems of the sequential discrimination of hypotheses for a compound Poisson process with exponential jumps. Optimal stopping games for Markov processes. A game-theoretic version of an optimal stopping problem. Séminaire de Probabilités XXXVIII, 5-15, Lecture Notes in Math., 1857, Springer, Berlin, 2005. Some excursion calculations for spectrally one-sided Lévy processes. Backward stochastic differential equations with reflection and Dynkin games. Perpetual American options under Lévy processes. Cambridge University Press, Cambridge, 2002. Encyclopedia of Mathematics and its Applications, 89. Cambridge University Press, Cambridge, 1996. ![]() The Shepp-Shiryaev stochastic game driven by a spectrally negative Lévy process. ![]() Fluctuation Theory and Stochastic Games for Spectrally Negative Lévy Processes. Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options. Some remarks on first passage of Lévy processes, the American put and pasting principles.
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