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The book Sustainable Management of Natural Resource: Mathematical Modeling exhibits and develops quantitative and formal links between sustainable development issues, decision and precaution problems in the management of natural resource. Mathematical or numerical modeling and methods presented here rely on control theory of dynamical systems. Applied concerns include fisheries, agriculture, biodiversity, exhaustible resource and pollution. Drawn from teachings given at several French interdisciplinary formations dealing with environmental economics, ecology and conservation biology, the book aims at reconciling economic and ecological dimensions through a common modeling framework to cope with these environmental management problems in a sustainability perspective.
Thus a particular attention is paid to multi-criteria issue and intergenerational equity. Regarding the interdisciplinary goal, in order to simplify the mathematical content, the proposed models and methods are restricted to the framework of discrete time dynamics. This allows for a direct entry into ecology for life-cycle, age classes and meta-population with patches. Similarly in economics, it favors a straightforward account of the framework of decision under uncertainty. In the same vein, particular attention has been paid to propose numerous examples, together with many figures and associated computer programs (written in Scilab, a "Matlab-like" free scientific software). Main approaches presented in the book are equilibrium and stability, viability and invariance, inter-temporal optimality going from discounted utilitarian to Rawlsian criteria. For these methods, both deterministic, stochastic and robustframeworks are examined. The case of imperfect information is also introduced at the end. The book mixes well-known material and applications with new insights especially from viability and robust analysis.
From the contents Sequential Decision Models.- Equilibrium and Stability.- Viable Sequential Decisions.- Optimal Sequential Decisions.- Sequential Decisions under Uncertainty.- Robust and Stochastic Viability.- Robust and Stochastic Optimization.- Sequential Decision under Imperfect Information.- Appendix. Mathematical Proofs.- Index.