The influence of Knightian uncertainty on sustainable financial welfare consequences

This study investigates the consequences of sustainable financial welfare based on the Knightian uncertainty framework. First, the dynamic equations of enterprise capital stock, portfolio return, and agent wealth are characterized by using G-Brownian motion. Second, the Hamilton–Jacobi–Bellman (HJB) equations satisfied by the value functions of both the enterprise and agent are derived by using the principle of optimality under sublinear expectation. Then, first-order conditions (FOCs) and ordinary differential equations (ODEs) that satisfy the optimal investment, disaster mitigation expenditure, and welfare measure are derived. Finally, the steady-state values of the variables and their trajectories over time under different levels of Knightian uncertainty were obtained through MATLAB numerical simulation. Additionally, the steady-state values and trajectories of the variables under the jump shock scenario (Hong, H., Wang, N., & Yang, J. Q. (2023b). Welfare consequences of sustainable finance. The Review of Financial Studies, 36(12), 4864–4918. https://doi.org/10.1093/rfs/hhad048) were compared with those under the Knightian uncertainty scenario. The study found that the economy under Knightian uncertainty accumulates more decarbonization capital and has a higher welfare level than the jump shock scenario. Moreover, as Knightian uncertainty increases, the optimal decarbonization capital stock decreases, and the economy's welfare level also declines accordingly.