Solutions of semi-Markov control models with recursive discount rates and approximation by ϵ-optimal policies

Title:

Solutions of semi-Markov control models with recursive discount rates and approximation by ϵ-optimal policies

Creator:

García , Yofre H. and González-Hernández, Juan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:22500c5a-0c95-45e7-9336-a305c8fe148c
uuid:22500c5a-0c95-45e7-9336-a305c8fe148c
doi:10.14736/kyb-2019-3-0495

Subject:

dynamic programming method, optimal stochastic control, and semi-Markov processes

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

This paper studies a class of discrete-time discounted semi-Markov control model on Borel spaces. We assume possibly unbounded costs and a non-stationary exponential form in the discount factor which depends of on a rate, called the discount rate. Given an initial discount rate the evolution in next steps depends on both the previous discount rate and the sojourn time of the system at the current state. The new results provided here are the existence and the approximation of optimal policies for this class of discounted Markov control model with non-stationary rates and the horizon is finite or infinite. Under regularity condition on sojourn time distributions and measurable selector conditions, we show the validity of the dynamic programming algorithm for the finite horizon case. By the convergence in finite steps to the value functions, we guarantee the existence of non-stationary optimal policies for the infinite horizon case and we approximate them using non-stationary ϵ−optimal policies. We illustrated our results a discounted semi-Markov linear-quadratic model, when the evolution of the discount rate follows an appropriate type of stochastic differential equation.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

495-517

Source:

Kybernetika | 2019 Volume:55 | Number:3

Harvested from:

CDK

Metadata only:

false