Optimal stopping for Lévy processes and affine functions

Details Optimal stopping for Lévy processes and affine functions Optimal stopping for Lévy processes and affine functions

2008-04-21

arxiv.org/abs/0804.3277v1

Mathematics

Probability

32 pages

Scientific paper

This paper studies an optimal stopping problem for L\'evy processes. We give a justification of the form of the Snell envelope using standard results of optimal stopping. We also justify the convexity of the value function, and without a priori restriction to a particular class of stopping times, we deduce that the smallest optimal stopping time is necessarily a hitting time. We propose a method which allows to obtain the optimal threshold. Moreover this method allows to avoid long calculations of the integro-differential operatorused in the usual proofs.

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