Defensive Resource Allocation: The Roles of Forecast Information and Risk Control.

In defensive resource allocation problems, the defender usually collects some forecast information about the attacker. However, the forecast information may be incorrect, which means that there could be a risk associated with the defender using it in their decision making. In this article, we propose a forecast and risk control (FRC) framework to manage the risk in defensive resource allocation with forecast information. In the FRC framework, we introduce a new measure of risk and three types of defense plans: riskless defense plan, risky defense plan, and risk-control defense plan. Several desirable properties based on the concepts of reward and penalty show that the risk-control defense plan is a general form to support defensive resource allocation. Subsequently, we study a specific defensive allocation problem with forecast information and develop an optimization model that considers the forecast information and the defender's risk tolerance level in order to obtain the risk-control defense plan with maximum reward. Furthermore, we provide some numerical analysis to illustrate the effects of forecast information and risk tolerance level on the risk-control defense plan. Finally, a numerical case study is presented to demonstrate the usability of a risk-control defense plan.