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Optimal Control Approaches to Sustainability under Uncertainty

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  • Phoebe Koundouri
  • Georgios I. Papayiannis
  • Athanasios Yannacopoulos

Abstract

Optimal sustainable management of natural resources has been one of the major lines of research in environmental economics at least for the last two decades. Several attempts have been made in order to describe in a quantitative fashion the notion of sustainability and distinguish management policies between sustainable and non sustainable ones. Important aspects of this task are (a) appropriate modeling of the spatio-temporal dynamics of the state of the system, including the sources of uncertainty affecting either directly or indirectly the problem at hand (e.g. climate conditions, population growth, biological evolution, etc), and (b) the development of appropriate criteria for evaluating the welfare of the system under study that guarantee sustainability and viability. In this chapter, we present and discuss popular and established optimization approaches for investigating policy selection problems within the sustainability framework, from the perspective of viability and optimal control theory.

Suggested Citation

  • Phoebe Koundouri & Georgios I. Papayiannis & Athanasios Yannacopoulos, 2022. "Optimal Control Approaches to Sustainability under Uncertainty," DEOS Working Papers 2215, Athens University of Economics and Business.
    • Handle: RePEc:aue:wpaper:2215
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    1. Christian Gollier & Phoebe Koundouri & Theologos Pantelidis, 2008. "Declining discount rates: Economic justifications and implications for long-run policy [‘Regime switches in interest rates’]," Economic Policy, CEPR, CESifo, Sciences Po;CES;MSH, vol. 23(56), pages 758-795.
    2. Martinet, Vincent, 2011. "A characterization of sustainability with indicators," Journal of Environmental Economics and Management, Elsevier, vol. 61(2), pages 183-197, March.
    3. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
    4. N. Englezos & X. Kartala & P. Koundouri & M. Tsionas & A. Alamanos, 2023. "A Novel HydroEconomic - Econometric Approach for Integrated Transboundary Water Management Under Uncertainty," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 84(4), pages 975-1030, April.
    5. Kenneth Arrow & Partha Dasgupta & Lawrence Goulder & Gretchen Daily & Paul Ehrlich & Geoffrey Heal & Simon Levin & Karl-Göran Mäler & Stephen Schneider & David Starrett & Brian Walker, 2004. "Are We Consuming Too Much?," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 147-172, Summer.
    6. Doyen, L. & Martinet, V., 2012. "Maximin, viability and sustainability," Journal of Economic Dynamics and Control, Elsevier, vol. 36(9), pages 1414-1430.
    7. Alan Randall, 2020. "On Intergenerational Commitment, Weak Sustainability, and Safety," Sustainability, MDPI, vol. 12(13), pages 1-18, July.
    8. Alvarez-Cuadrado, Francisco & Van Long, Ngo, 2009. "A mixed Bentham-Rawls criterion for intergenerational equity: Theory and implications," Journal of Environmental Economics and Management, Elsevier, vol. 58(2), pages 154-168, September.
    9. Elettra Agliardi, 2011. "Sustainability in Uncertain Economies," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 48(1), pages 71-82, January.
    10. Wolfgang Buchholz & Swapan Dasgupta & Tapan Mitra, 2005. "Intertemporal Equity and Hartwick's Rule in an Exhaustible Resource Model," Scandinavian Journal of Economics, Wiley Blackwell, vol. 107(3), pages 547-561, September.
    11. Vincent Martinet & Julio Peña-Torres & Michel Lara & Hector Ramírez C., 2016. "Risk and Sustainability: Assessing Fishery Management Strategies," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 64(4), pages 683-707, August.
    12. Asheim, Geir B. & Mitra, Tapan, 2010. "Sustainability and discounted utilitarianism in models of economic growth," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 148-169, March.
    13. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "Growth and agglomeration in the heterogeneous space: a generalized AK approach," Journal of Economic Geography, Oxford University Press, vol. 19(6), pages 1287-1318.
    14. d'Autume, Antoine & Schubert, Katheline, 2008. "Hartwick's rule and maximin paths when the exhaustible resource has an amenity value," Journal of Environmental Economics and Management, Elsevier, vol. 56(3), pages 260-274, November.
    15. Karp, Larry, 2007. "Non-constant discounting in continuous time," Journal of Economic Theory, Elsevier, vol. 132(1), pages 557-568, January.
    16. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    17. Noël Bonneuil & Raouf Boucekkine, 2014. "Viable Ramsey economies," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 47(2), pages 422-441, May.
    18. R. M. Solow, 1974. "Intergenerational Equity and Exhaustible Resources," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 29-45.
    19. Phoebe Koundouri & Theologos Pantelidis & Ben Groom & Ekaterini Panopoulou, 2007. "Discounting the distant future: How much does model selection affect the certainty equivalent rate?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(3), pages 641-656.
    20. Rabi Bhattacharya & Hyeonju Kim & Mukul Majumdar, 2015. "Sustainability in the Stochastic Ramsey Model," Papers 1511.07419, arXiv.org.
    21. W.A. Brock & A. Xepapadeas & A.N. Yannacopoulos, 2014. "Optimal Control in Space and Time and the Management of Environmental Resources," Annual Review of Resource Economics, Annual Reviews, vol. 6(1), pages 33-68, October.
    22. Greaves, Hilary, 2017. "Discounting For Public Policy: A Survey," Economics and Philosophy, Cambridge University Press, vol. 33(3), pages 391-439, November.
    23. Athanassoglou, Stergios & Xepapadeas, Anastasios, 2012. "Pollution control with uncertain stock dynamics: When, and how, to be precautious," Journal of Environmental Economics and Management, Elsevier, vol. 63(3), pages 304-320.
    24. Martinet, V. & Doyen, L., 2007. "Sustainability of an economy with an exhaustible resource: A viable control approach," Resource and Energy Economics, Elsevier, vol. 29(1), pages 17-39, January.
    25. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    26. Xepapadeas, A. & Yannacopoulos, A.N., 2016. "Spatial growth with exogenous saving rates," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 125-137.
    27. Hepburn, Cameron J. & Koundouri, Phoebe, 2007. "Recent advances in discounting: Implications for forest economics," Journal of Forest Economics, Elsevier, vol. 13(2-3), pages 169-189, August.
    28. Holger Strulik, 2021. "Hyperbolic discounting and the time‐consistent solution of three canonical environmental problems," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(3), pages 462-486, June.
    29. Zuber, Stéphane & Asheim, Geir B., 2012. "Justifying social discounting: The rank-discounted utilitarian approach," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1572-1601.
    30. Mitra, Tapan & Roy, Santanu, 2017. "Optimality of Ramsey–Euler policy in the stochastic growth model," Journal of Economic Theory, Elsevier, vol. 172(C), pages 1-25.
    31. Phoebe Koundouri & Christina Christou, 2006. "Dynamic adaptation to resource scarcity and backstop availability: theory and application to groundwater ," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 50(2), pages 227-245, June.
    32. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    33. World Commission on Environment and Development,, 1987. "Our Common Future," OUP Catalogue, Oxford University Press, number 9780192820808.
    34. Xanthi-Isidora Kartala & Nikolaos Englezos & Athanasios N. Yannacopoulos, 2020. "Future Expectations Modeling, Random Coefficient Forward–Backward Stochastic Differential Equations, and Stochastic Viscosity Solutions," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 403-433, May.
    35. W. Brock & A. Xepapadeas & A. Yannacopoulos, 2014. "Robust Control and Hot Spots in Spatiotemporal Economic Systems," Dynamic Games and Applications, Springer, vol. 4(3), pages 257-289, September.
    36. Partha Dasgupta & Eric Maskin, 2005. "Uncertainty and Hyperbolic Discounting," American Economic Review, American Economic Association, vol. 95(4), pages 1290-1299, September.
    37. Withagen, Cees & B. Asheim, Geir, 1998. "Characterizing sustainability: The converse of Hartwick's rule," Journal of Economic Dynamics and Control, Elsevier, vol. 23(1), pages 159-165, September.
    38. Dixit, Avinash K., 1990. "Optimization in Economic Theory," OUP Catalogue, Oxford University Press, edition 2, number 9780198772101.
    39. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    40. Brock, William & Xepapadeas, Anastasios, 2010. "Pattern formation, spatial externalities and regulation in coupled economic-ecological systems," Journal of Environmental Economics and Management, Elsevier, vol. 59(2), pages 149-164, March.
    41. Hediger, Werner, 2000. "Sustainable development and social welfare," Ecological Economics, Elsevier, vol. 32(3), pages 481-492, March.
    42. Ben Groom & Cameron Hepburn & Phoebe Koundouri & David Pearce, 2005. "Declining Discount Rates: The Long and the Short of it," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 32(4), pages 445-493, December.
    43. Graciela Chichilnisky, 1996. "An axiomatic approach to sustainable development," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(2), pages 231-257, April.
    44. Panas, Epaminondas & Yannacopoulos, Athanasios N., 2012. "Ramsey meets Laibson and Itô: Effects of hyperbolic discounting on stochastic growth," The Journal of Economic Asymmetries, Elsevier, vol. 9(1), pages 51-65.
    45. Rajagopal, 2014. "Technology Diffusion and Adoption," Palgrave Macmillan Books, in: Architecting Enterprise, chapter 6, pages 148-173, Palgrave Macmillan.
    46. Robert C. Merton, 1975. "An Asymptotic Theory of Growth Under Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 375-393.
    47. Margarita Genius & Phoebe Koundouri & Céline Nauges & Vangelis Tzouvelekas, 2014. "Information Transmission in Irrigation Technology Adoption and Diffusion: Social Learning, Extension Services, and Spatial Effects," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 96(1), pages 328-344.
    48. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    49. Phoebe Koundouri & Céline Nauges & Vangelis Tzouvelekas, 2006. "Technology Adoption under Production Uncertainty: Theory and Application to Irrigation Technology," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 88(3), pages 657-670.
    50. Martin L. Weitzman, 1997. "Sustainability and Technical Progress," Scandinavian Journal of Economics, Wiley Blackwell, vol. 99(1), pages 1-13, March.
    51. Partha Dasgupta & Geoffrey Heal, 1974. "The Optimal Depletion of Exhaustible Resources," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 3-28.
    52. Fabio Antoniou & Panos Hatzipanayotou & Phoebe Koundouri, 2012. "Second Best Environmental Policies under Uncertainty," Southern Economic Journal, John Wiley & Sons, vol. 78(3), pages 1019-1040, January.
    53. Georgios I. Papayiannis, 2022. "Robust Policy Selection and Harvest Risk Quantification for Natural Resources Management under Model Uncertainty," Papers 2202.05326, arXiv.org.
    54. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    55. Amilon, Henrik & Bermin, Hans-Peter, 2003. "Welfare effects of controlling labor supply: an application of the stochastic Ramsey model," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 331-348, November.
    56. Yannacopoulos, Athanasios N., 2008. "Rational expectations models: An approach using forward-backward stochastic differential equations," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 251-276, February.
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    Keywords

    Model Uncertainty; Optimal Control; Robust Optimal Control; Sustain- ability; Viability Theory;
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