Discrete-time Markov control processes with recursive discount rates

Yofre H. García; Juan González-Hernández

Kybernetika (2016)

  • Volume: 52, Issue: 3, page 403-426
  • ISSN: 0023-5954

Abstract

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This work analyzes a discrete-time Markov Control Model (MCM) on Borel spaces when the performance index is the expected total discounted cost. This criterion admits unbounded costs. It is assumed that the discount rate in any period is obtained by using recursive functions and a known initial discount rate. The classic dynamic programming method for finite-horizon case is verified. Under slight conditions, the existence of deterministic non-stationary optimal policies for infinite-horizon case is proven. Also, to find deterministic non-stationary ϵ - optimal policies, the value-iteration method is used. To illustrate an example of recursive functions that generate discount rates, we consider the expected values of stochastic processes, which are solutions of certain class of Stochastic Differential Equations (SDE) between consecutive periods, when the initial condition is the previous discount rate. Finally, the consumption-investment problem and the discount linear-quadratic problem are presented as examples; in both cases, the discount rates are obtained using a SDE, similar to the Vasicek short-rate model.

How to cite

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H. García, Yofre, and González-Hernández, Juan. "Discrete-time Markov control processes with recursive discount rates." Kybernetika 52.3 (2016): 403-426. <http://eudml.org/doc/281537>.

@article{H2016,
abstract = {This work analyzes a discrete-time Markov Control Model (MCM) on Borel spaces when the performance index is the expected total discounted cost. This criterion admits unbounded costs. It is assumed that the discount rate in any period is obtained by using recursive functions and a known initial discount rate. The classic dynamic programming method for finite-horizon case is verified. Under slight conditions, the existence of deterministic non-stationary optimal policies for infinite-horizon case is proven. Also, to find deterministic non-stationary $\epsilon -$optimal policies, the value-iteration method is used. To illustrate an example of recursive functions that generate discount rates, we consider the expected values of stochastic processes, which are solutions of certain class of Stochastic Differential Equations (SDE) between consecutive periods, when the initial condition is the previous discount rate. Finally, the consumption-investment problem and the discount linear-quadratic problem are presented as examples; in both cases, the discount rates are obtained using a SDE, similar to the Vasicek short-rate model.},
author = {H. García, Yofre, González-Hernández, Juan},
journal = {Kybernetika},
keywords = {dynamic programming method; optimal stochastic control},
language = {eng},
number = {3},
pages = {403-426},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Discrete-time Markov control processes with recursive discount rates},
url = {http://eudml.org/doc/281537},
volume = {52},
year = {2016},
}

TY - JOUR
AU - H. García, Yofre
AU - González-Hernández, Juan
TI - Discrete-time Markov control processes with recursive discount rates
JO - Kybernetika
PY - 2016
PB - Institute of Information Theory and Automation AS CR
VL - 52
IS - 3
SP - 403
EP - 426
AB - This work analyzes a discrete-time Markov Control Model (MCM) on Borel spaces when the performance index is the expected total discounted cost. This criterion admits unbounded costs. It is assumed that the discount rate in any period is obtained by using recursive functions and a known initial discount rate. The classic dynamic programming method for finite-horizon case is verified. Under slight conditions, the existence of deterministic non-stationary optimal policies for infinite-horizon case is proven. Also, to find deterministic non-stationary $\epsilon -$optimal policies, the value-iteration method is used. To illustrate an example of recursive functions that generate discount rates, we consider the expected values of stochastic processes, which are solutions of certain class of Stochastic Differential Equations (SDE) between consecutive periods, when the initial condition is the previous discount rate. Finally, the consumption-investment problem and the discount linear-quadratic problem are presented as examples; in both cases, the discount rates are obtained using a SDE, similar to the Vasicek short-rate model.
LA - eng
KW - dynamic programming method; optimal stochastic control
UR - http://eudml.org/doc/281537
ER -

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