scholarly journals On group analysis of optimal control problems in economic growth models

2020 ◽  
Vol 13 (10) ◽  
pp. 2853-2876
Author(s):  
Gülden Gün Polat ◽  
◽  
Teoman Özer ◽  
Keyword(s):  
Economic Growth ◽  
Optimal Control ◽  
Optimal Control Problems ◽  
Growth Models ◽  
Group Analysis ◽  
Control Problems ◽  
Economic Growth Models

ASYMPTOTICS OF VALUE FUNCTION IN MODELS OF ECONOMIC GROWTH

2018 ◽  
pp. 605-616
Author(s):  
Alexander Leonidovich Bagno ◽  
Alexander Mikhailovich Tarasyev
Keyword(s):  
Economic Growth ◽  
Optimal Control ◽  
Asymptotic Behavior ◽  
Value Function ◽  
Growth Models ◽  
Infinite Horizon ◽  
Minimax Solution ◽  
Growth Stability ◽  
Economic Growth Models ◽  
The Value Function

Asymptotic behavior of the value function is studied in an infinite horizon optimal control problem with an unlimited integrand index discounted in the objective functional. Optimal control problems of such type are related to analysis of trends of trajectories in models of economic growth. Stability properties of the value function are expressed in the infinitesimal form. Such representation implies that the value function coincides with the generalized minimax solution of the Hamilton–Jacobi equation. It is shown that that the boundary condition for the value function is substituted by the property of the sublinear asymptotic behavior. An example is given to illustrate construction of the value function as the generalized minimax solution in economic growth models.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Sign in / Sign up

Export Citation Format

Share Document