Based on the ideas of a game theoretical model presented in the paper "The Timing and Deterrence of Terrorist Attacks" by Kjell Hausken and Jun Zhuang, in this thesis a nonlinear optimal control model is formulated, which is linked to an ongoing conflict in Colombia. In this framework the decision maker has to decide wether to invest a normalised budget into the security level of an asset he tries to defend against an attacker or directly into the asset in form of repairs or upgrades. The second player of the game theoretical model will be modeled as an exogenous force in form of a "reaction function". This nonlinear optimal control model then will be solved by applying Pontryagin's Maximum Principle.
The main goal of this thesis is to analyse how different kinds of attackers affect the model results and optimal solutions. In a first step simple, strictly monotone and strictly convex (concave) reaction functions will be applied. For a given set of parameters values, which will model a well organised attacker, the problem will be solved and a sensitivity analysis will be carried out. In an extension, more complex, convex-concave (concave-convex) reaction functions will be used and it will be analysed how they affect the model outcome.