[{"type":"article-journal","title":"Stochastic Dynamic Programming with Non-linear Discounting","issued":{"date-parts":[["2020"]]},"container-title":"Applied mathematics & optimization","DOI":"10.1007\/s00245-020-09731-x","author":[{"family":"B\u00e4uerle","given":"Nicole"},{"family":"Ja\u015bkiewicz","given":"Anna"},{"family":"Nowak","given":"Andrzej S."}],"publisher":"Springer","ISSN":"0095-4616, 1432-0606","abstract":"In this paper, we study a Markov decision process with a non-linear discount function and with a Borel state space. We define a recursive discounted utility, which resembles non-additive utility functions considered in a number of models in economics. Non-additivity here follows from non-linearity of the discount function. Our study is complementary to the work of Ja\u015bkiewicz et al. (Math Oper Res 38:108\u2013121, 2013), where also non-linear discounting is used in the stochastic setting, but the expectation of utilities aggregated on the space of all histories of the process is applied leading to a non-stationary dynamic programming model. Our aim is to prove that in the recursive discounted utility case the Bellman equation has a solution and there exists an optimal stationary policy for the problem in the infinite time horizon. Our approach includes two cases: (a) when the one-stage utility is bounded on both sides by a weight function multiplied by some positive and negative constants, and (b) when the one-stage utility is unbounded from below.","keyword":"Stochastic dynamic programming; Non-linear discounting; Bellman equation; Optimal stationary policy","kit-publication-id":"1000129381"}]