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.

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.

scholarly journals Analysis of Economic Growth Models via Value Function Design

2018 ◽  
Vol 51 (32) ◽  
pp. 624-629
Author(s):  
Alexander L. Bagno ◽  
Alexander M. Tarasyev
Keyword(s):  
Economic Growth ◽  
Value Function ◽  
Growth Models ◽  
Function Design ◽  
Economic Growth Models

scholarly journals Optimal control of piecewise deterministic Markov processes: a BSDE representation of the value function

2018 ◽  
Vol 24 (1) ◽  
pp. 311-354 ◽  
Author(s):  
Elena Bandini
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Markov Processes ◽  
Value Function ◽  
Backward Stochastic Differential Equation ◽  
Infinite Horizon ◽  
Random Measure ◽  
Uniqueness Results ◽  
Piecewise Deterministic Markov Processes ◽  
The Value Function

We consider an infinite-horizon discounted optimal control problem for piecewise deterministic Markov processes, where a piecewise open-loop control acts continuously on the jump dynamics and on the deterministic flow. For this class of control problems, the value function can in general be characterized as the unique viscosity solution to the corresponding Hamilton−Jacobi−Bellman equation. We prove that the value function can be represented by means of a backward stochastic differential equation (BSDE) on infinite horizon, driven by a random measure and with a sign constraint on its martingale part, for which we give existence and uniqueness results. This probabilistic representation is known as nonlinear Feynman−Kac formula. Finally we show that the constrained BSDE is related to an auxiliary dominated control problem, whose value function coincides with the value function of the original non-dominated control problem.

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