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
which guarantees a growing total wealth
. 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.
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