TITLE:
Asymptotic Evaluations of the Stability Index for a Markov Control Process with the Expected Total Discounted Reward Criterion
AUTHORS:
Jaime Eduardo Martínez-Sánchez
KEYWORDS:
Control Consumption-Investment Process, Discrete-Time Markov Control Process, Expected Total Discounted Reward, Probabilistic Metrics, Stability Index Estimation
JOURNAL NAME:
American Journal of Operations Research,
Vol.11 No.1,
January
28,
2021
ABSTRACT: In this
work, for a control consumption-investment process with the discounted reward
optimization criteria, a numerical estimate of the stability index is made.
Using explicit formulas for the optimal stationary policies and for the value
functions, the stability index is explicitly calculated and through statistical
techniques its asymptotic behavior is investigated (using numerical
experiments) when the discount coefficient approaches 1. The results obtained define
the conditions under which an approximate optimal stationary policy can be used
to control the original process.