Mathematical modeling of distributed catastrophic and terrorist risks

The paper shows how the mathematical tools of the theory of controlled Markov fields can be applied to model catastrophic risks caused by natural events or terrorist threats. The examples of problem statements of long-term investment in security are given. 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 quasigradient method

A Risk-Informed Decision-Making Framework for Climate Change Adaptation through Robust Land Use and Irrigation Planning

Uncertainty and variability are key challenges for climate change adaptation planning. In the face of uncertainty, decision-making can be addressed in two interdependent stages: make only partial ex ante anticipative actions to keep options open until new information is revealed, and adapt the first-stage decisions with respect to newly acquired information. This decision-making approach corresponds to the two-stage stochastic optimization (STO) incorporating both anticipative ex ante and adaptive ex post decisions within a single model. This paper develops a two-stage STO model for climate change adaptation through robust land use and irrigation planning under conditions of uncertain water supply. The model identifies the differences between decision-making in the cases of perfect information, full uncertainty, and two-stage STO from the perspective of learning about uncertainty. Two-stage anticipative and adaptive decision-making with safety constraints provides risk-informed decisions characterized by quantile-based Value-at-Risk and Conditional Value-at-Risk risk measures. The ratio between the ex ante and ex post costs and the shape of uncertainty determine the balance between the anticipative and adaptive decisions. Selected numerical results illustrate that the alteration of the ex ante agricultural production costs can affect crop production, management technologies, and natural resource utilization