[...]... Mathematical Proofs 237 A.1 Mathematical proofs of Chap 3 237 A.2 Mathematical proofs of Chap 4 239 A.3 Mathematical proofs of Chap 5 244 A.4 Robust and stochastic dynamic programming equations 248 A.5 Mathematical proofs of Chap 7 252 A.6 Mathematical proofs of Chap... notions of sustainable development and the precautionary principle 2 1 Introduction Exhaustible resources One of the main initial environmental debates deals with the use and management of exhaustible resource such as coal and oil In 1972, the Club of Rome published a famous report, “The Limits to Growth” [28], arguing that unlimited economic growth is impossible because of the exhaustibility of some resources. .. contrary of an abstention rule This observation raises at least two main questions Why does indecision exist a priori ? How can such indecision be overcome? At this stage, the impact of the resolution of uncertainties on the timing of action appears as a touchstone of precaution Mathematical and numerical modeling From this brief panorama of numerous issues related to the management of natural resources, ... non-compliance of agents or by by-catch related to multi-species management are important The difficulties in the usual management of renewable resources have led some recent works to advocate the use of ecosystemic approaches [5, 8] as a central element of future resource management This framework aims at capturing a major part of the complexity of the systems in a relevant way encompassing, in particular,... indicators for fisheries management ICES Journal of Marine Science, 62:307– 614, 2005 [9] P Dasgupta The Control of Ressources Basil Blackwell, Oxford, 1982 [10] P Dasgupta and G Heal The optimal depletion of exhaustible resources Review of Economic Studies, 41:1–28, 1974 Symposium on the Economics of Exhaustible Resources [11] M De Lara, L Doyen, T Guilbaud, and M.-J Rochet Is a management framework based... Practice of Population Viability Analysis Sinauer Associates, 2003 [30] C Mullon, P Cury, and L Shannon Viability model of trophic interactions in marine ecosystems Natural Resource Modeling, 17:27–58, 2004 [31] L J Olson and R Santanu Dynamic efficiency of conservation of renewable resources under uncertainty Journal of Economic Theory, 95:186– 214, 2000 [32] D Pezzey Economic analysis of sustainable. .. of an exhaustible resource might limit economic growth These works have pointed out that substitutability features of natural resources are decisive in a production system economy Moreover the question of intergenerational equity appears as a central point in such works Renewable resources Renewable resources are under extreme pressure worldwide despite efforts to design better regulation in terms of. .. sophisticated and complex Integrated models are, however, required for the management of natural resources Unfortunately, the models of each scientific area do not combine in a straightforward manner For instance, difficulties may occur in defining common scales of time or space Furthermore, the addition of several models extends the dimensions of the problem and makes it complicated or impossible to solve Ecological,... R M Solow Intergenerational equity and exhaustible resources Review of Economic Studies, 41:29–45, 1974 Symposium on the Economics of Exhaustible Resources [39] J Stiglitz Growth with exhaustible natural resources: Efficient and optimal growth paths Review of Economic Studies, 41:123–137, 1974 Symposium on the Economics of Exhaustible Resources [40] WCED Our common Future Oxford University Press, 1987... policy: What difference have we made Journal of Environmental Economics and Management, 39:306–327, 2000 [42] P Yodzis Predator-prey theory and management of multispecies fisheries Ecological Applications, 4(1):51–58, February 1994 2 Sequential decision models Although the management of exhaustible and renewable resources and pollution control are issues of a different nature, their main structures are . assessment, the conservation and the management of natural resources. This monograph, Sustainable Management of Natural Resources, Mathe- matical Models and. assess- ment, conservation and management of natural resources are induced by such preoccupations. The problems confronted in sustainable management share certain