Uniqueness of the solution of Bellman's equation in the case of general controlled processes
type: Item
instance of: scholarly article
title: Uniqueness of the solution of Bellman's equation in the case of general controlled processes
zbMATH Open document ID: 0568.49010
DOI: 10.1007/BF00969616
published in: Lithuanian Mathematical Journal
publication date: 1982-01-01T00:00:00Z
review text: In a previous paper by the author [Litov. Mat. Sb. 21, No.4, 169-184 (1981; Zbl 0489.49011)] it is proved that in the case of controlled stochastic processes consisting of diffusion, drift, and jump components, the payoff function satisfies Bellman's equation, which is a nonlinear singular integrodifferential equation in the lattice of measures. In the present paper we study the question of uniqueness of the solution of Bellman's equation. The paper consists of three sections. In the first section the notation and assumptions are introduced and the basic result of the paper is formulated. In the second and third sections a probabilistic representation of the solution of Bellman's equation is developed and with the help of this representation the basic theorem of the paper is proved.
Mathematics Subject Classification ID: 49J55
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 28A15
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 3907218
zbMATH Keywords: controlled stochastic processes
zbMATH Keywords: diffusion
zbMATH Keywords: drift
zbMATH Keywords: jump components
zbMATH Keywords: payoff function
zbMATH Keywords: Bellman's equation
zbMATH Keywords: nonlinear singular integrodifferential equation
zbMATH Keywords: lattice of measures
author: Henrikas Pragarauskas
MaRDI profile type: Publication
cites work: Q3951128
cites work: Q4190545
cites work: Q3658831
cites work: Q4118565
cites work: Q4162249
cites work: Q3955254
cites work: Q5524051
description: scientific article; zbMATH DE number 3907218