Optimal linear-quadratic regulator for a stochastic system under mutually inverse time preferences in the cost

E. S. Palamarchuk<sup>ab

a</sup> Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
^b National Research University "Higher School of Economics", Moscow

Abstract: We investigate a long-run behavior of a linear stochastic system. It is assumed that the quadratic cost includes a time-varying function and its multiplicative inverse. Such a specification reflects the fact that time preferences used by agents to assess different types of losses evolve in opposite directions. We consider the case when priority is set for the losses associated with state deviations. The optimal control law is derived with respect to extended long-run average cost criteria. We provide conditions for the existence of an alternative control strategy, which is also optimal and is based on a solution of an algebraic Riccati equation.

Keywords: linear regulator of a stochastic system, time preferences, long-run average.

MSC: 93E20 49N10 60H10

Received: 02.04.2022
Revised: 10.10.2022
Accepted: 10.10.2022

DOI: 10.4213/tvp5567

 English version: Theory of Probability and its Applications, 2023, 68:1, 31–45

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