@techreport{Sennewald2005Controlled,
abstract = {The present paper is concerned with the optimal control of stochastic differential equations, where uncertainty stems
from one or more independent Poisson processes. Optimal behavior in such a setup (e.g., optimal consumption) is
usually determined by employing the Hamilton-Jacobi-Bellman equation. This, however, requires strong assumptions
on the model, such as a bounded utility function and bounded coefficients in the controlled differential equation. The
present paper relaxes these assumptions. We show that one can still use the Hamilton-Jacobi-Bellman equation as a
necessary criterion for optimality if the utility function and the coefficients are linearly bounded. We also derive
sufficiency in a verification theorem without imposing any boundedness condition at all. It is finally shown that, under
very mild assumptions, an optimal Markov control is optimal even within the class of general controls.},
author = {Ken Sennewald},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
keywords = {C61; 330; Stochastic differential equation; Poisson process; Bellman equation; Kontrolltheorie; Analysis; Stochastischer Prozess; Zeitpr\"{a}ferenz; Theorie},
language = {eng},
number = {03/05},
title = {Controlled Stochastic Differential Equations under Poisson Uncertainty and with Unbounded Utility},
type = {Dresden discussion paper in economics},
url = {http://hdl.handle.net/10419/22720},
year = {2005}
}