Optimal stopping time problem in a general framework

By M. Kobylanski, Marie Claire Quenez. 2012

62 citations recorded by the source corpus.

We study the optimal stopping time problem $v(S)={\rm ess}\sup_{\theta \geq S} E[\phi(\theta)|\mathcal{F}_S]$, for any stopping time $S$,  where the reward is given by a family $(\phi(\theta),\theta\in\mathcal{T}_0)$ \emph{of non negative random variables} indexed by stopping times. We solve the problem under weak assumptions in terms of integrability and regularity of the reward family. More precisely, we only suppose $v(0) < + \infty$ and $(\phi(\theta),\theta\in \mathcal{T}_0)$ upper semicontinuous along stopping times in expectation. We show the existence of an optimal stopping time and obtain a characterization of the minimal and the maximal optimal stopping times. We also provide some local properties of the value function family. All the results are written in terms of families of random variables and are proven by only using classical results of the Probability Theory

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/73ad802baacec7301dfd0f07fc3ca612df8fed1b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Demography

1. Peter Imkeller
2. Miryana Grigorova
3. Y. Ouknine
4. Marie Claire Quenez
5. Adrien Richou

In Finance

1. Peter Imkeller
2. Y. Ouknine
3. Miryana Grigorova
4. E. Offen
5. Marie Claire Quenez
6. Alexander Schied
7. Massimiliano Gubinelli
8. Lukasz Delong

In Management Science and Operations Research

1. Peter Imkeller
2. Miryana Grigorova
3. Y. Ouknine
4. Marie Claire Quenez
5. E. Offen
6. Alexander Schied
7. Daniel Hernandez-Hernandez
8. P. Briand

Citations in the corpus

• Reflected BSDEs when the obstacle is not right-continuous and optimal stopping (2015, background): “[27], [11], [21], [22]), some tools from the general theory of processes (cf.”
• Reflected BSDEs and robust optimal stopping for dynamic risk measures with jumps (2012, unknown): “11 in [14] (or [6]), we have ∫ T 0 (Y t − ξt)dAt = 0 a.”
• Optimal stopping with f-expectations: The irregular case (2016, background): “10 in [28] also holds true in the case where the reward process is not necessarily nonnegative.”