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Environmental management and restoration should be designed such that therisk and uncertainty owing to nonlinear stochastic systems can be successfullyaddressed. We apply the robustified dynamic Orlicz risk to the modeling andanalysis of environmental management and restoration to consider both the riskand uncertainty within a unified theory. We focus on the control of ajump-driven hybrid stochastic system that represents macrophyte dynamics. Thedynamic programming equation based on the Orlicz risk is first obtainedheuristically, from which the associated Hamilton-Jacobi-Bellman (HJB) equationis derived. In the proposed Orlicz risk, the risk aversion of thedecision-maker is represented by a power coefficient that resembles a certaintyequivalence, whereas the uncertainty aversion is represented by theKullback-Leibler divergence, in which the risk and uncertainty are handledconsistently and separately. The HJB equation includes a new state-dependentdiscount factor that arises from the uncertainty aversion, which leads to aunique, nonlinear, and nonlocal term. The link between the proposed andclassical stochastic control problems is discussed with a focus oncontrol-dependent discount rates. We propose a finite difference method forcomputing the HJB equation. Finally, the proposed model is applied to anoptimal harvesting problem for macrophytes in a brackish lake that containsboth growing and drifting populations.

Environmental management and restoration under unified risk and uncertainty using robustified dynamic Orlicz risk