scholarly journals The value-function of an infinite-horizon linear-quadratic problem

2003 ◽  
Vol 16 (1) ◽  
pp. 71-78 ◽  
Author(s):  
J. Blot ◽  
P. Michel
Keyword(s):  
Value Function ◽  
Infinite Horizon ◽  
Linear Quadratic ◽  
Quadratic Problem ◽  
The Value Function

scholarly journals Stochastic optimal control problem with infinite horizon driven by G-Brownian motion

2018 ◽  
Vol 24 (2) ◽  
pp. 873-899 ◽  
Author(s):  
Mingshang Hu ◽  
Falei Wang
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Value Function ◽  
Infinite Horizon ◽  
Dynamic Programming Principle ◽  
Stochastic Optimal Control Problem ◽  
The Value Function

The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the unique viscosity solution of the related Hamilton−Jacobi−Bellman−Isaacs (HJBI) equation.

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.

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