Time-consistent stopping under decreasing impatience

Arrêt temporellement cohérent sous impatience décroissante

Yu-Jui Huang (1) , Adrien Nguyen-Huu (2)

1 University of Colorado - Department of Applied Mathematics
2 LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée

Under non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for equilibrium stopping policies, formulated as fixed points of an operator. Under appropriate conditions, fixed-point iterations converge to equilibrium stopping policies. This iterative approach corresponds to the hierarchy of strategic reasoning in Game Theory, and provides ``agent-specific'' results: it assigns one specific equilibrium stopping policy to each agent according to her initial behavior. In particular, it leads to a precise mathematical connection between the naive behavior and the sophisticated one. Our theory is illustrated in a real options model.

Mots clés: Time-inconsistency; Optimal Stopping; Decreasing impatience; Hyperbolic discounting; subgame perfect equilibrium; sequential game

Domaines: Optimisation et contrôle [math.OC]; Gestion des risques [q-fin.RM]

Yu-Jui Huang, Adrien Nguyen-Huu. Time-consistent stopping under decreasing impatience. 2017. ⟨hal-01116414v4⟩