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On the Fixed Points of the Optimal Reward Operator in Stochastic Dynamic Programming with Discount Factor Greater than One
Author(s) -
Hübner Gerhard
Publication year - 1977
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19770570808
Subject(s) - fixed point , discounting , dynamic programming , operator (biology) , mathematics , value (mathematics) , mathematical optimization , markov decision process , time horizon , point (geometry) , bellman equation , fixed point iteration , markov process , economics , statistics , mathematical analysis , finance , biochemistry , chemistry , geometry , repressor , transcription factor , gene
It is well‐known that in case of a discount factor β < 1 the optimal reward operator has a unique fixed point which equals the value of the infinite horizon problem. If β > 1 this is in general not true, but a fixed point may nevertheless exist. The existence of a unique fixed point is proved under some additional condition and a method of successive approximation is given. Applications of this algorithm and of policy iteration to estimates for values of the finite stage problems and for the turnpike planning horizon are discussed.