6533b7d0fe1ef96bd125a0a0

RESEARCH PRODUCT

Monotone Concave Operators: An application to the existence and uniqueness of solutions to the Bellman equation

Cuong Le VanLisa MorhaimYiannis Vailakis

subject

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Dynamic programmingBellman equationUnbounded returnsjel:C61JEL: C61 O41[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][SHS.ECO]Humanities and Social Sciences/Economics and FinanceDynamic programmingjel:O41Bellman equationUnbounded returnsDynamic Programming; Bellman Equation; Unbounded Returns[ SHS.ECO ] Humanities and Social Sciences/Economies and finances[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC][SHS.ECO] Humanities and Social Sciences/Economics and Finance

description

We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel’skii (1964) and Krasnosel’skii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone concave operators defined on partially order spaces.

yearjournalcountryeditionlanguage
2008-07-28
https://hal.archives-ouvertes.fr/hal-00294828/file/Final-07-04-08.pdf