Electronic Communications in Probability

On the strict value of the non-linear optimal stopping problem

Abstract

We address the non-linear strict value problem in the case of a general filtration and a completely irregular pay-off process $(\xi _{t})$. While the value process $(V_{t})$ of the non-linear problem is only right-uppersemicontinuous, we show that the strict value process $(V^{+}_{t})$ is necessarily right-continuous. Moreover, the strict value process $(V_{t}^{+})$ coincides with the process of right-limits $(V_{t+})$ of the value process. As an auxiliary result, we obtain that a strong non-linear $f$-supermartingale is right-continuous if and only if it is right-continuous along stopping times in conditional $f$-expectation.

Article information

Source
Electron. Commun. Probab., Volume 25 (2020), paper no. 49, 9 pp.

Dates
Accepted: 18 June 2020
First available in Project Euclid: 18 July 2020

https://projecteuclid.org/euclid.ecp/1595037888

Digital Object Identifier
doi:10.1214/20-ECP328

Citation

Grigorova, Miryana; Imkeller, Peter; Ouknine, Youssef; Quenez, Marie-Claire. On the strict value of the non-linear optimal stopping problem. Electron. Commun. Probab. 25 (2020), paper no. 49, 9 pp. doi:10.1214/20-ECP328. https://projecteuclid.org/euclid.ecp/1595037888

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