Published in Finance and Stochastics (Volume 22).
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.
After discussing the weaknesses of the aggregated statistical approach to estimate economic damage, we conclude that, if these functions cannot reasonably be trusted for such a large cooling, they should not be considered to provide relevant information on potential damage in the case of a warming of similar magnitude, as projected in the case...