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A controller-stopper-game with hidden controller type

Andi Bodnariu and Kristoffer Lindensjö

Stochastic Processes and their Applications, 2024, vol. 173, issue C

Abstract: We consider a continuous time stochastic dynamic game between a stopper (the owner of an asset) and a controller (the manager) who is either effective or non-effective. An effective manager can exert high or low effort which corresponds to a high or a low positive drift for the accumulated income of the owner with random noise in terms of Brownian motion. The manager earns a salary until the owner stops the game. A non-effective manager cannot act but receives a salary. We find a threshold (Nash) equilibrium using stochastic filtering methods in a weak formulation.

Date: 2024
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DOI: 10.1016/j.spa.2024.104361

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