Existence results for Isaacs equations with local conditions and related semilinear Cauchy problems

Abstract

Our goal is to prove existence results for classical solutions to some general nondegenerate Cauchy problems which are natural generalizations of Isaacs equations. For the latter we are able to extend our results by admitting local conditions for coefficients. Such equations appear naturally for instance in robust control theory. Using our general results, we can solve not only Isaacs equations, but also equations for other sophisticated control problems, for instance models with state dependent constraints on the control set.

Stochastic control on the half-line and applications to the optimal dividend/consumption problem

“…Note that the space C 1,0 b together with • κ forms a Banach space. The norm is inspired by previous works on the parabolic Cauchy problems and is usualy applied to the consumption -investment problem: Becherer and Schweizer [2], Delong and Klüppelberg [4], Berdjane and Pergamenshchikov [3] and Zawisza [12]. But only the last paper have used such type of norm to consider equations with nonlinearities in the gradient part.…”