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

On large deviations in estimation problem with dependent observations

The paper is devoted to the stochastic optimization problem with a stationary ergodic random sequence satisfying the hypermixing condition. It is assumed that we have the finite number of observed elements in the sequence, and instead of solving the former problem we investigate the empirical function, find its points of minimum, and study their asymptotic properties. More precisely we consider the probabilities of large deviations of minimizers and the minimal value of the empirical criterion function from the corresponding characteristics of the main problem. The conditions under which the probabilities of the large deviations decrease exponentially are found

Development of Robust Land-use Decisions in Eastern Europe under Technology, Climate, and System Change: The Case of Ukraine

The states of Eastern Europe (Ukraine and all the adjacent European states Belarus, Hungary, Moldova, Poland, Romania, Slovakia) have experienced technology and system change in land use since the 1990s. Their total land area exceeds the land area of Mexico or Indonesia, their total gross domestic product (in current US dollars) is between those products of Mexico and Indonesia, and their total population is higher than population of the Russian Federation or Japan. Some Eastern European states are in the world top-five producers of corn, rye, oat, triticale, buckwheat, potato, carrot, turnip, apple, gooseberry, raspberry, blueberry, plum, currant, milk (sheep), honey, flax, and other agricultural goods. It is found the agricultural production value of Romania, Slovakia, and Ukraine has higher efficiency (in the terms of water and energy use) than that of Belarus, Moldova, Poland, and Hungary. Therefore, it was expected the regions of Ukraine bordering with Romania and Slovakia are of the highest agricultural productivity. This hypothesis is confirmed by the data of capital and labor use as well as the data of agricultural production value. At the lack of energy resources, in Ukraine water appears to be a critical agricultural production factor. Moreover, the regions of Ukraine experiencing a water deficit happened to be the most vulnerable ones substantiating the well-known hypothesis on growing role of water resources for sustainable development. Because a water demand depends on the weather conditions and climate changes, the robust land-use decisions are to be developed in order to contribute to the world food security. For instance, Ukraine is transforming from a global breadbasket to a global foodbasket attracting significant investments to food production and export. The strategic investments and operational land-use decisions are based on such modern systemic risk measures as (conditional) value-at-risk, robust variant of mean or maximum loss

Mathematical Modeling of Agricultural Crop Diversification in Ukraine: Scientific Approaches and Empirical Results*

The paper describes an agricultural crop diversification model on the basis of simulation modeling and robust solutions. The model is intended for the design and development of the optimal structure of crop areas in order to combine the agricultural crops in a compatible manner, and to gradually transition to the principles of sustainable farming in domestic agriculture. A detailed analysis of the modern practice of monoculture farming was conducted. Based on these calculations, a diversified structure of ten agricultural crops is proposed, which will help strengthen the internal food security and harmonize agricultural development in its ecological, social, and economic aspects

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