(Alneelain University, 2015-07) Ranya Hamid El Nour
ABSTRACT.
The aim of this thesis is to study and solve optimal control problems for systems driven by
both: Brownian motion and Levy processes. The methods of solution used are: Dynamic
programming, and Maximum principle where the known Clark-Ocone theorem is applied. The
application of Clark-Ocone theorem needs the existence of Malliavin derivative and its extesion
in L2 spaces. As an application , the thesis considered an example of harvesting problem in a
crowded media as well as searching for optimal portfolio strategies in hedging options in markets
driven by both: Brovmian motion and Levy processes.
