Uniqueness of the solution of Bellman's equation in the case of general controlled processes
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.
nonlinear singular integrodifferential equation
scientific article; zbMATH DE number 3907218