An iterative method for multiple stopping problem under Knightian uncertainty

H. Li^ab, H. Liu<sup>c

a</sup> Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Shandong, P. R. China
^b Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Shandong University, Shandong, P. R. China
^c School of Economics, Ocean University of China, Shandong, P. R. China

Abstract: In this paper, we introduce a new algorithm based on the one-step improvement to solve the optimal multiple stopping problem under Knightian uncertainty in the discrete time case. This algorithm induces a monotonically increasing sequence to approximate the value functions, which coincides with the value functions after finitely many iteration steps independent of the times of exercise rights. We also present the stability of this algorithm and some numerical simulations.

Keywords: optimal multiple stopping, Knightian uncertainty, $g$-expectation, one-step improvement.

MSC: 60G40

Received: 14.07.2023
Accepted: 26.05.2024

DOI: 10.4213/tvp5671

 English version: Theory of Probability and its Applications, 2025, 70:1, 92–112

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