Skip to main content
SpringerLink
Log in

Optimal Control Approaches to Sustainability Under Uncertainty

  • Living reference work entry
  • First Online:
SDGs in the European Region

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), and (b) the development of appropriate criteria for evaluating the welfare of the system under study that guarantees 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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Alvarez-Cuadrado F, Van Long N (2009) A mixed Bentham-Rawls criterion for intergenerational equity: theory and implications. J Environ Econ Manag 58(2):154–168

    Article  Google Scholar 

  • Amilon H, Bermin HP (2003) Welfare effects of controlling labor supply: an application of the stochastic Ramsey model. J Econ Dyn Control 28(2):331–348

    Article  Google Scholar 

  • Antoniou F, Hatzipanayotou P, Koundouri P (2012) Second best environmental policies under uncertainty. South Econ J 78(3):1019–1040

    Article  Google Scholar 

  • Arrow KJ, Dasgupta P, Mäler KG (2003) Evaluating projects and assessing sustainable development in imperfect economies. Environ Resour Econ 26(4):647–685

    Article  Google Scholar 

  • Asheim GB (2010) Justifying, characterizing and indicating sustainability. Springer Science & Business Media

    Google Scholar 

  • Asheim GB, Ekeland I (2016) Resource conservation across generations in a Ramsey-Chichilnisky model. Economic Theory 61(4):611–639

    Article  Google Scholar 

  • Asheim GB, Mitra T (2010) Sustainability and discounted utilitarianism in models of economic growth. Math Soc Sci 59(2):148–169

    Article  Google Scholar 

  • Asheim GB, Buchholz W, Withagen C (2007) The Hartwick rule: myths and facts. In: Justifying, characterizing and indicating sustainability. Springer, Dordrecht, pp 125–145

    Chapter  Google Scholar 

  • Athanassoglou S, Xepapadeas A (2012) Pollution control with uncertain stock dynamics: when, and how, to be precautious. J Environ Econ Manag 63(3):304–320

    Article  Google Scholar 

  • Aubin J-P, Bayen AM, Saint-Pierre P (2011) Viability theory: new directions. s

    Book  Google Scholar 

  • Baltas I, Xepapadeas A, Yannacopoulos AN (2019) Robust control of parabolic stochastic partial differential equations under model uncertainty. Eur J Control 46:1–13

    Article  Google Scholar 

  • Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press

    Book  Google Scholar 

  • Bhattacharya R, Kim H, Majumdar M (2015) Sustainability in the stochastic Ramsey model. J Quant Econ 13(2):169–184

    Article  Google Scholar 

  • Boucekkine R, Camacho C, Fabbri G (2013) Spatial dynamics and convergence: the spatial AK model. J Econ Theory 148(6):2719–2736

    Article  Google Scholar 

  • Boucekkine R, Fabbri G, Federico S, Gozzi F (2019) Growth and agglomeration in the heterogeneous space: a generalized AK approach. J Econ Geogr 19(6):1287–1318

    Article  Google Scholar 

  • Brock W, Xepapadeas A (2010) Pattern formation, spatial externalities and regulation in coupled economic-ecological systems. J Environ Econ Manag 59(2):149–164

    Article  Google Scholar 

  • Brock WA, Xepapadeas A, Yannacopoulos AN (2014a) Optimal control in space and time and the management of environmental resources. Annu Rev Resour Econ 6(1):33–68

    Article  Google Scholar 

  • Brock WA, Xepapadeas A, Yannacopoulos AN (2014b) Robust control and hot spots in spatiotemporal economic systems. Dyn Games Appl 4(3):257–289

    Article  Google Scholar 

  • Buchholz W, Dasgupta S, Mitra T (2005) Intertemporal equity and Hartwick’s rule in an exhaustible resource model. Scand J Econ 107(3):547–561

    Article  Google Scholar 

  • Chichilnisky G (1996) An axiomatic approach to sustainable development. Soc Choice Welf 13(2):231–257

    Article  Google Scholar 

  • Ciriacy-Wantrup SV (1968) Resource conservation: economics and policies. University of California Press

    Google Scholar 

  • d’Autume A, Schubert K (2008) Hartwick’s rule and maximin paths when the exhaustible resource has an amenity value. J Environ Econ Manag 56(3):260–274

    Article  Google Scholar 

  • Dasgupta P, Heal G (1974) The optimal depletion of exhaustible resources. Rev Econ Stud 41:3–28

    Article  Google Scholar 

  • Dasgupta P, Maskin E (2005) Uncertainty and hyperbolic discounting. Am Econ Rev 95(4):1290–1299

    Article  Google Scholar 

  • Dixit AK, Sherrerd JJ (1990) Optimization in economic theory. Oxford University Press

    Google Scholar 

  • Doyen L, Gajardo P (2020) Sustainability standards, multicriteria maximin, and viability. Nat Resour Model 33(3):e12250

    Article  Google Scholar 

  • Doyen L, Martinet V (2012) Maximin, viability and sustainability. J Econ Dyn Control 36(9):1414–1430

    Article  Google Scholar 

  • Ekeland I, Lazrak A (2010) The golden rule when preferences are time inconsistent. Math Finan Econ 4(1):29–55

    Article  Google Scholar 

  • Ekeland I, Long Y, Zhou Q (2013) A new class of problems in the calculus of variations. Regul Chaotic Dyn 18(6):553–584

    Article  Google Scholar 

  • Englezos N, Kartala X, Koundouri P, Tsionas M, Alamanos A (2021) A novel hydro-economic-econometric approach for integrated transboundary water management under uncertainty. Athens University of Economics and Business

    Google Scholar 

  • Fabbri G, Gozzi F, Swiech A (2017) Stochastic optimal control in infinite dimension. Probability and stochastic modelling. Springer

    Book  Google Scholar 

  • Frederick S, Loewenstein G, O’donoghue, T. (2002) Time discounting and time preference: a critical review. J Econ Lit 40(2):351–401

    Article  Google Scholar 

  • Genius M, Koundouri P, Nauges C, Tzouvelekas V (2014) Information transmission in irrigation technology adoption and diffusion: social learning, extension services, and spatial effects. Am J Agric Econ 96(1):328–344

    Article  Google Scholar 

  • Gollier C (2012) Pricing the planet’s future. Princeton University Press

    Book  Google Scholar 

  • Gollier C, Koundouri P, Pantelidis T (2008) Declining discount rates: economic justifications and implications for long-run policy. Econ Policy 23(56):758–795

    Article  Google Scholar 

  • Greaves H (2017) Discounting for public policy: a survey. Econ Philos 33(3):391–439

    Article  Google Scholar 

  • Groom B, Hepburn C, Koundouri P, Pearce D (2005) Declining discount rates: the long and the short of it. Environ Resour Econ 32(4):445–493

    Article  Google Scholar 

  • Groom B, Koundouri P, Panopoulou E, Pantelidis T (2007) Discounting the distant future: how much does model selection affect the certainty equivalent rate? J Appl Econ 22(3):641–656

    Article  Google Scholar 

  • Gutés MC (1996) The concept of weak sustainability. Ecol Econ 17(3):147–156

    Article  Google Scholar 

  • Hansen L, Sargent TJ (2001) Robust control and model uncertainty. Am Econ Rev 91(2):60–66

    Article  Google Scholar 

  • Hansen LP, Sargent TJ (2011) Robustness. Princeton University Press

    Google Scholar 

  • Hediger W (2000) Sustainable development and social welfare. Ecol Econ 32(3):481–492

    Article  Google Scholar 

  • Hediger W (2006) Weak and strong sustainability, environmental conservation and economic growth. Nat Resour Model 19(3):359–394

    Article  Google Scholar 

  • Hepburn CJ, Koundouri P (2007) Recent advances in discounting: implications for forest economics. J For Econ 13(2–3):169–189

    Google Scholar 

  • Karp L (2007) Non-constant discounting in continuous time. J Econ Theory 132(1):557–568

    Article  Google Scholar 

  • Kartala XI, Englezos N, Yannacopoulos AN (2020) Future expectations modeling, random coefficient forward-backward stochastic differential equations, and stochastic viscosity solutions. Math Oper Res 45(2):403–433

    Article  Google Scholar 

  • Knight FH (1921) Risk, uncertainty and profit. Houghton Mifflin, Boston

    Google Scholar 

  • Koundouri P (2004) Potential for groundwater management: Gisser–Sanchez effect reconsidered. Water Resour Res 40(6)

    Google Scholar 

  • Koundouri P, Christou C (2006) Dynamic adaptation to resource scarcity and backstop availability: theory and application to groundwater. Aust J Agric Resour Econ 50(2):227–245

    Article  Google Scholar 

  • Koundouri P, Nauges C, Tzouvelekas V (2006) Technology adoption under production uncertainty: theory and application to irrigation technology. Am J Agric Econ 88(3):657–670

    Article  Google Scholar 

  • Laibson D (1997) Golden eggs and hyperbolic discounting. Q J Econ 112(2):443–478

    Article  Google Scholar 

  • Marinacci M (2015) Model uncertainty. J Eur Econ Assoc 13(6):1022–1100

    Article  Google Scholar 

  • Martinet V (2011) A characterization of sustainability with indicators. J Environ Econ Manag 61(2):183–197

    Article  Google Scholar 

  • Martinet V, Doyen L (2007) Sustainability of an economy with an exhaustible resource: a viable control approach. Resour Energy Econ 29:17–39

    Article  Google Scholar 

  • Martinet V, Pena-Torres J, De Lara M, Ramírez CH (2016) Risk and sustainability: assessing fishery management strategies. Environ Resour Econ 64(4):683–707

    Article  Google Scholar 

  • Merton RC (1975) An asymptotic theory of growth under uncertainty. Rev Econ Stud 42(3):375–393

    Article  Google Scholar 

  • Mitra T, Roy S (2017) Optimality of Ramsey: Euler policy in the stochastic growth model. J Econ Theory 172:1–25

    Article  Google Scholar 

  • Panas E, Yannacopoulos AN (2012) Ramsey meets Laibson and Itô: effects of hyperbolic discounting on stochastic growth. J Econ Asymmetries 9(1):51–65

    Article  Google Scholar 

  • Papayiannis GI (2022) Robust policy selection and harvest risk quantification for natural resources management under model uncertainty. J Dynd Games 9(2):203–217

    Article  Google Scholar 

  • Papayiannis GI, Yannacopoulos AN (2018) Convex risk measures for the aggregation of multiple information sources and applications in insurance. Scand Actuar J 2018(9):792–822

    Article  Google Scholar 

  • Petracou EV, Xepapadeas A, Yannacopoulos AN (2021) Decision making under model uncertainty: Fréchet -Wasserstein mean preferences. Manag Sci 68(2):1195–1211

    Article  Google Scholar 

  • Pflug GC, Pichler A (2014) Multistage stochastic optimization. Springer International Publishing, Cham

    Book  Google Scholar 

  • Portney PR, Weyant JP (2013) Discounting and intergenerational equity. Routledge

    Book  Google Scholar 

  • Ramsey F (1928) A mathematical model of savings. Econ J 38(152):543–559

    Article  Google Scholar 

  • Randall A (2020) On intergenerational commitment, weak sustainability, and safety. Sustainability 12(13):5381

    Article  Google Scholar 

  • Rawls J (1972) A theory of justice. Cambridge University Press, Cambridge

    Google Scholar 

  • Solow RM (1974) Intergenerational equity and exhaustible resources. Rev Econ Stud 41:29–45

    Article  Google Scholar 

  • Solow RM (1986) On the intergenerational allocation of natural resources. Scand J Econ 88:141–149

    Article  Google Scholar 

  • Strulik H (2021) Hyperbolic discounting and the time-consistent solution of three canonical environmental problems. J Public Econ Theory 23(3):462–486

    Article  Google Scholar 

  • Vinter RB (2010) Optimal control. Birkhäuser, Boston

    Book  Google Scholar 

  • WCED (World Commission on Environment and Development) (1987) Our common future. Oxford University Press, Oxford

    Google Scholar 

  • Weitzman ML (1997) Sustainability and technical progress. Scand J Econ 99(1):1–13

    Article  Google Scholar 

  • Withagen C, Asheim GB (1998) Characterizing sustainability: the converse of Hartwick’s rule. J Econ Dyn Control 23(1):159–165

    Article  Google Scholar 

  • Xepapadeas A, Yannacopoulos AN (2016) Spatial growth with exogenous saving rates. J Math Econ 67:125–137

    Article  Google Scholar 

  • Yannacopoulos AN (2008) Rational expectations models: an approach using forward-backward stochastic differential equations. J Math Econ 44(3–4):251–276

    Article  Google Scholar 

  • Yong J, Zhou XY (1999) Stochastic controls: Hamiltonian systems and HJB equations. Springer Science & Business Media

    Book  Google Scholar 

  • Zuber S, Asheim GB (2012) Justifying social discounting: the rank-discounted utilitarian approach. J Econ Theory 147(4):1572–1601

    Article  Google Scholar 

Download references

Acknowledgments

The authors wish to thank Professor A. Xepapadeas (Bologna and AUEB) for useful and insightful comments on this manuscript. This paper is a result of the project Water-Futures which has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant agreement No. 951424).

Author information

Authors and Affiliations

  1. School of Economics, Athens University of Economics & Business, Athens, Greece

    P. Koundouri

  2. ReSEES Laboratory, Athens University of Economics & Business, Athens, Greece

    P. Koundouri

  3. Department of Technology, Management & Economics, Technical University of Denmark, Lyngby, Denmark

    P. Koundouri

  4. Sustainable Development Unit and EIT Climate-KIC, ATHENA Information Technologies RC, Marousi, Greece

    P. Koundouri

  5. UN Sustainable Development Solutions Network, Europe, Paris, France

    P. Koundouri

  6. Department of Naval Sciences, Section of Mathematics, Mathematical Modelling and Applications Laboratory, Hellenic Naval Academy, Piraeus, Greece

    G. I. Papayiannis

  7. Stochastic Modelling and Applications Laboratory, Athens University of Economics & Business, Athens, Greece

    G. I. Papayiannis & A. N. Yannacopoulos

  8. School of Information Sciences & Technology, Department of Statistics, Athens University of Economics & Business, Athens, Greece

    A. N. Yannacopoulos

Authors
  1. P. Koundouri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. I. Papayiannis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. N. Yannacopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Koundouri .

Editor information

Editors and Affiliations

  1. European School of Sustainability, Hamburg University of Applied Sciences, Hamburg, Hamburg, Germany

    Walter Leal Filho

  2. UFP Energy, Environment and Health Research Unit (FP-ENAS), University Fernando Pessoa (UFP), Porto, Portugal

    Maria Alzira Pimenta Dinis

  3. University of Verona, Verona, Italy

    Sara Moggi

  4. Manchester Metropolitan University, Manchester, UK

    Elizabeth Price

  5. Newcastle Business School, Northumbria University, Newcastle upon Tyne, UK

    Alex Hope

Section Editor information

  1. Department of Geography and Environmental Sciences, Northumbria University at Newcastle upon Tyne, Newcastle upon Tyne, UK

    Richard Kotter

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Koundouri, P., Papayiannis, G.I., Yannacopoulos, A.N. (2022). Optimal Control Approaches to Sustainability Under Uncertainty. In: Leal Filho, W., Dinis, M.A.P., Moggi, S., Price, E., Hope, A. (eds) SDGs in the European Region . Implementing the UN Sustainable Development Goals – Regional Perspectives. Springer, Cham. https://doi.org/10.1007/978-3-030-91261-1_46-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-91261-1_46-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-91261-1

  • Online ISBN: 978-3-030-91261-1

  • eBook Packages: Springer Reference Earth and Environm. ScienceReference Module Physical and Materials ScienceReference Module Earth and Environmental Sciences

Publish with us

Policies and ethics

Search

Navigation