An optimal hostage rescue problem

This paper proposes the following mathematical models for an optimal rescue problem concerning hostages. Suppose that persons are taken hostage at a given point of time. A decision to attempt either to rescue or no rescue has to be made. In the paper we mainly consider two different objectives: Minimization of the expected number of hostages being killed and maximization of the probability of no hostage being killed. Several properties of an optimal rescuing rule are revealed.