2015/02/13 by Yu‐Jui Huang, Huang, Yu-Jui, Adrien Nguyen Huu +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Capital Investment and Risk Analysis #FOS: Mathematics #Optimization and Control (math.OC) #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.1502.03998
openalex publication_date 2015/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.