Open Access
2020 On the strict value of the non-linear optimal stopping problem
Miryana Grigorova, Peter Imkeller, Youssef Ouknine, Marie-Claire Quenez
Electron. Commun. Probab. 25: 1-9 (2020). DOI: 10.1214/20-ECP328


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.


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Miryana Grigorova. Peter Imkeller. Youssef Ouknine. Marie-Claire Quenez. "On the strict value of the non-linear optimal stopping problem." Electron. Commun. Probab. 25 1 - 9, 2020.


Received: 6 January 2020; Accepted: 18 June 2020; Published: 2020
First available in Project Euclid: 18 July 2020

zbMATH: 07252769
MathSciNet: MR4125796
Digital Object Identifier: 10.1214/20-ECP328

Primary: 60G07 , 60G40 , 91G80

Keywords: general filtration , irregular payoff , non-linear expectation , Optimal stopping , strict value process , strong $\mathcal {E}^{f}$-supermartingale

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