# Kristofer Lindensjö: How to detect a salami slicer: a stochastic controller-stopper game with unknown competition

**Time: **
Wed 2022-03-09 15.15 - 16.00

**Location: **
Kräftriket, House 6, Room 306

**Lecturer: **
Kristofer Lindensjö (Stockholm University)

### Abstract

A stochastic controller-stopper game for fraud detection is introduced. A process X(t)=−θΛ(t)+W(t) represents the holdings of an account holder (player 1), where θΛ(t) is the accumulated amount stolen by a fraudster (player 2) and θ is a Bernoulli random variable indicating whether the fraudster is active or not, and W(t) is a Brownian motion. The fraudster seeks to choose the fraud strategy process Λ(t) that maximizes the expected discounted amount stolen whereas the account holder – who observes only the path of X(t) and hence cannot know if fraud occurs – seeks to choose a stopping time that deactivates the fraudster, at cost M>0, and minimizes the expected discounted cost of fraud and deactivation. By developing a stochastic filtering method, we find explicit Nash equilibria of both pure and mixed type. Based on joint work with Erik Ekström (Uppsala university) and Marcus Olofsson (Umeå university).