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Pré-Publication, Document De Travail Année : 2010

Optimal stopping with discontinuous reward

Résumé

We study, for any stopping time $S$, the optimal stopping time problem $v(S)= \esssup_{\theta \geq S} E[\phi(\theta)|\F_S]$, where the reward is given by a family $\{\phi(\theta),\TO\}$ {\em of positive random variables} indexed by stopping times. We solve the problem under the weakest assumptions in terms of the regularity of the reward. More precisely, the reward family $\{\phi(\theta),\TO\}$ is supposed to satisfy some compatibility conditions and to be upper-semicontinuous along stopping times in expectation. We give several properties of the value function. We show the existence of an optimal stopping time. Also, we obtain a characterization of the minimal and the maximal optimal stopping times.

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Dates et versions

hal-00519457 , version 1 (20-09-2010)
hal-00519457 , version 2 (27-09-2010)
hal-00519457 , version 3 (27-02-2013)

Identifiants

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Magdalena Kobylanski, Marie-Claire Quenez. Optimal stopping with discontinuous reward. 2010. ⟨hal-00519457v2⟩
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