Volume 27, 2021
|Number of page(s)||18|
|Published online||03 March 2021|
Controlled Markov chains with non-exponential discounting and distribution-dependent costs*
Department of Statistics, Rice University,
2 Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA.
** Corresponding author: firstname.lastname@example.org
Accepted: 2 January 2021
This paper deals with a controlled Markov chain in continuous time with a non-exponential discounting and distribution-dependent cost functional. A definition of closed-loop equilibrium is given and its existence and uniqueness are established. Due to the time-inconsistency brought by the non-exponential discounting and distribution dependence, it is proved that the equilibrium is locally optimal in some appropriate sense. Moreover, it is shown that our problem is equivalent to a mean-field game for infinite-many symmetric players with a non-exponential discounting cost.
Mathematics Subject Classification: 93E20 / 60J27 / 90C40
Key words: time inconsistency / distribution dependence / controlled Markov chain
© EDP Sciences, SMAI 2021
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