CS40: Dynamical Systems Modelling
Organizer: Anna Jaśkiewicz & Krzysztof Szajowski (Wrocław University of Science and Technology)
Multiple Stopping Porosinski’s Problem
Aiko Kurushima
We consider the multiple stopping version of the full-information best choice problem with a random number of observations. The single stopping case was previously solved by Porosinski (1987), who addressed the problem of maximizing the probability of selecting the overall maximum from a sequence of independent and identically distributed random variables drawn from the uniform distribution. He derived the optimal stopping rule under certain assumptions on the distribution of the random horizon.In this talk, we extend the setting to allow multiple stopping opportunities. We explore the conditions on the distribution required for optimality and present an optimal multiple stopping strategy under a stronger assumption on the distribution.
Multiple Stopping Problems and Their Applications
Georgy Sofronov
In many applications data are sequentially collected over time, and it is necessary to make decisions based on already obtained information while future observations are not known yet. Formally speaking, we observe a sequence of random variables and have to decide when we must stop, given that there is no recall allowed, that is, a random variable once rejected cannot be chosen later on; for further details, see \([1]\). Our decision to stop depends on the observations already made, but does not depend on the future which is not yet known. In this talk, we will give an overview of discrete-time problems when at least two stops are required.
Bibliography
\([1]\) Sofronov, G., & Szajowski, K. (2025). Multiple Stopping Problems: Unilateral and Multilateral Approaches. CRC Press, Taylor & Francis Group.
On the stopping problem of Markov chain and Odds-theorem
Hitosi Inui
We discusses several aspects of the proof of the Odds-theorem in terms of several complementary remarks. Our main point will be that the optimality of the Odds-strategy is also characterized by a discrete version the Dynkin formula which we introduce in this paper. This is closely linked to with the so-called monotone case of optimal stopping problem.