TITLE:
Adaptive Investment Strategies for Transitioning from Fossil-Fuels to Cleaner Energies: An Application of Conjugate Utilities
AUTHORS:
Gaoganwe Sophie Moagi, Obonye Doctor, Edward Lungu
KEYWORDS:
Energy Transition, Sustainable Finance, Conjugate Utility Theory, Girsanov Theorem, Stochastic Differential Equations, Portfolio Optimization
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.16 No.2,
April
2,
2026
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.