Necessity of the terminal condition in the infinite horizon dynamic optimization problems with unbounded payoff

Do not Blame Bellman: It Is Koopmans' Fault

“…Recently, Rincón‐Zapatero (2024) extended this method to a stochastic environment. Le Van and Morhaim (2002), Le Van and Vailakis (2005), Kamihigashi (2014), and Wiszniewska‐Matyszkiel and Singh (2021) proposed a more primitive transversality condition to identify an appropriate space of candidate value functions. Jaśkiewisz and Nowak (2011) and Matkowski and Nowak (2011) presented a systematic study of all these approaches under uncertainty.…”

An Approximation Approach to Dynamic Programming With Unbounded Returns

“…An alternative Local Contraction approach is presented by Rincón-Zapatero and Rodríguez-Palmero (2003) and Martins-da-Rocha and Vailakis (2010) to deal with aggregators that allow −∞ as a value. Another method followed by Le Van and Morhaim (2002), Le Van and Vailakis (2005), Kamihigashi (2014) and Wiszniewska-Matyszkiel and Singh (2021) abandons the contraction approach and looks directly for solutions to the Bellman's equation in a suitable space of functions satisfying a sort of transversality condition. Finally, a recent paper by Ma et al (2022) exploits a transformation of Bellman's operator, along with boundedness of the expected reward, to turn unbounded into bounded programs so that conventional contraction techniques apply.…”

Stability and existence of solutions to a class of Atangana-Baleanu-Caputo coupled fractional differential equations

“…Nowadays, some achievements have been made in the study of the existence of solutions of fractional order differential equations [30][31][32][33]. The terminal value problem is widely used in economics for risk control, dividend distribution, principal-agent and unbounded return dynamic optimization problems [34][35][36]. By numerically simulating the solution of the equation, we are able to solve problems in economics more clearly and accurately.…”