The next meeting of the National Seminar on Probability and Statistics will be held on November 3, 2024, at 3:00 p.m. in Room 503 of the Institute of Mathematics and Informatics. A talk on: Cancellable American options under negative discounting will be delivered by Zbigniew Palmowski (University of Wroclaw). Abstract. In this talk we consider the McKean stochastic game for a geometric spectrally negative Lévy process of asset price which extends the American put option by introducing the possibility for the writer of the option to cancel the contract, at the expense of paying the intrinsic value plus an extra constant penalty. Additionally, we consider a negative discount rate which produces double continuation regions for writer and holder. This is then different from the scenario [...]