Electronic Communications in Probability

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

Miryana Grigorova, Peter Imkeller, Youssef Ouknine, and Marie-Claire Quenez

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1595037888

Digital Object Identifier
doi:10.1214/20-ECP328

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60G07: General theory of processes 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)

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

Rights
Creative Commons Attribution 4.0 International License.

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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