This article is cited in 10 papers

MATHEMATICS

Properties of the value function in optimal control problems with infinite horizon

A. L. Bagno^a, A. M. Tarasyev<sup>b

a</sup> Department of Applied Mathematics, Ural Federal University, pr. Lenina, 51, Yekaterinburg, 620083, Russia
^b Department of Dynamic Systems, N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia

Abstract: The article investigates properties of the value function of the optimal control problem on infinite horizon with an unlimited integrand index appearing in the quality functional with a discount factor. The estimate is derived for approximating the value function in a problem with the infinite horizon by levels of value functions in problems with lengthening finite horizons. The structure of the value function is identified basing on stationary value functions which depend only on phase variables. The description is given for the asymptotic growth of the value function generated by various types of the quality functional applied in economic and financial modeling: logarithmic, power, exponential, linear functions. The property of continuity is specified for the value function and estimates are deduced for the Hölder parameters of continuity. These estimates are needed for the development of grid algorithms designed for construction of the value function in optimal control problems with infinite horizon.

Keywords: optimal control, infinite horizon, value function, estimation of continuity modulus, asymptotic properties.

UDC: 517.977

MSC: 49K15

Received: 27.10.2015

DOI: 10.20537/vm160101

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