Abstract. This paper shows the possibility of using the mathematical apparatus of the theory of controlled Markov fields to model catastrophe risks caused by natural events or terrorist threats. The examples are given for problem statements of long-term investment in safety. A survey of solution methods for stochastic optimal control problems is proposed. It is shown that these problems can be reduced to finite-dimensional stochastic programming problems and can be solved by the stochastic quasi-gradient method.

Keywords: catastrophic risk, terrorist threat, controlled Markov field, random field with local interaction, Gibbs field, stochastic programming, stochastic quasigradient method.