Research ArticleOpen AccessGoogle Scholar indexed
Adaptive Investment Strategies for Transitioning from Fossil-Fuels to Cleaner Energies: An Application of Conjugate Utilities
Department of Mathematics and Statistical Science, Botswana International University of Science and Technology, Palapye, Botswana
Department of Mathematics and Statistical Science, Botswana International University of Science and Technology, Palapye, Botswana
Department of Mathematics and Statistical Science, Botswana International University of Science and Technology, Palapye, Botswana
- 1 Department of Mathematics and Statistical Science, Botswana International University of Science and Technology, Palapye, Botswana
- 2 Department of Mathematics and Statistical Science, Botswana International University of Science and Technology, Palapye, Botswana
- 3 Department of Mathematics and Statistical Science, Botswana International University of Science and Technology, Palapye, Botswana
Journal of Mathematical Finance·Volume 16 (2026)·Pages 57–79·Published 1 May 2026·DOI10.4236/jmf.2026.162004
Copy link · social · email
Abstract
We have formulated an investment model that applies a conjugate utilities approach to illustrate that wealth can still grow in transitioning portfolios. We have proved that despite one asset being phased out, a unique solution for the wealth process exists. We have determined an optimal pair ( π 1 * , π 2 * ) which guarantees a growing total wealth W ( t ) . We have also shown that high stock volatility is detrimental to the return on investment. The results of this study indicate the possibility of portfolio replication while aligning with sustainable development goals, SDG7 and SDG13.
KeywordsEnergy TransitionSustainable FinanceConjugate Utility TheoryGirsanov TheoremStochastic Differential EquationsPortfolio Optimization
- United Nations Framework Convention on Climate Change. Key Aspects of the Paris Agreement. https://unfccc.int/most-requested/key-aspects-of-the-paris-agreement
- Glemarec, Y. (2010) Financing the Transition to a Low-Carbon Society. Journal of Renewable and Sustainable Energy , 2, Article ID: 031013. https://doi.org/10.1063/1.3459135
- Schoenmaker, D. and Schramade, W. (2019) Principles of Sustainable Finance. Oxford University Press.
- Agârbiceanu, S.M. and Păun, T. (2021) The Need for a Paradigm Shift in Finance: Sustainable Corporate Finance. Management of Sustainable Development , 13, 33-38. https://doi.org/10.54989/msd-2021-0006
- Balp, G. and Strampelli, G. (2022) Institutional Investor ESG Engagement: The European Experience. European Business Organization Law Review , 23, 869-904. https://doi.org/10.1007/s40804-022-00266-y
- Quitzow, L., Canzler, W., Grundmann, P., Leibenath, M., Moss, T. and Rave, T. (2016) The German Energiewende—What’s Happening? Introducing the Special Issue. Utilities Policy , 41, 163-171. https://doi.org/10.1016/j.jup.2016.03.002
- International Energy Agency (2024) World Energy Investment 2024. IEA. https://www.iea.org/reports/world-energy-investment-2024
- Goel, M. (2016) Solar Rooftop in India: Policies, Challenges and Outlook. Green Energy & Environment , 1, 129-137. https://doi.org/10.1016/j.gee.2016.08.003
- Government of Denmark. Pioneers in Clean Energy. https://denmark.dk/innovation-and-design/clean-energy
- Enerdata. Global Energy Trends (2021) https://www.enerdata.net/publications/reports-presentations/2021-energy-climate-trends.html
- Chaudhary, Y.C., Bangi, V.K.T., Guduru, R.K., Aung, K. and Reddy, G.N. (2017) Preliminary Investigation on Generation of Electricity Using Micro Wind Turbines Placed on a Car. International Journal of Renewable Energy Development , 6, 75-81. https://doi.org/10.14710/ijred.6.1.75-81
- Chen, J.M. (2021) The Capital Asset Pricing Model. Encyclopedia , 1, 915-933. https://doi.org/10.3390/encyclopedia1030070
- Feng, W., Bilivogui, P., Wu, J. and Mu, X. (2023) Green Finance: Current Status, Development, and Future Course of Actions in China. Environmental Research Communications , 5, Article ID: 035005. https://doi.org/10.1088/2515-7620/acc1c7
- Alamgir, M. and Cheng, M.-C. (2023) Do Green Bonds Play a Role in Achieving Sustainability? Sustainability , 15, Article No. 10177. https://doi.org/10.3390/su151310177