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<p>The sustainable management of renewable natural resources requires decision-making frameworks capable of accounting for both environmental and economic uncertainty. This paper develops a Real Options framework for fishing activity in which fish populations follow a stochastic Gompertz process and prices evolve according to a mean-reverting Geometric Ornstein–Uhlenbeck process. The valuation problem is formulated as a Hamilton–Jacobi–Bellman equation, solved numerically using a Crank–Nicolson finite difference scheme, and compared with an expected net present value approach under the same economic, biological, and adaptive harvesting assumptions, thereby isolating the effect of the valuation methodology. The results show that both approaches generate similar harvesting policies and population trajectories, with neither suggesting overexploitation over the simulated horizon. Nevertheless, the Real Options framework yields higher project values, primarily due to its treatment of systematic price risk. By linking risk compensation to a spanning asset rather than to an exogenous discount rate, it provides a more internally consistent valuation methodology. The comparison also reveals a trade-off between economic value and biological resilience, as the higher values obtained under the Real Options framework are associated with lower average population levels and greater dispersion in population outcomes. These findings highlight the relevance of Real Options methods for the economic valuation and sustainable management of renewable natural resources under uncertainty.</p>

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Stochastic differential equation models for harvesting: a valuation strategy assessment

  • 期刊论文

  • 发表日期：

    2026年7月20日

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  • Miguel Reis

摘要

The sustainable management of renewable natural resources requires decision-making frameworks capable of accounting for both environmental and economic uncertainty. This paper develops a Real Options framework for fishing activity in which fish populations follow a stochastic Gompertz process and prices evolve according to a mean-reverting Geometric Ornstein–Uhlenbeck process. The valuation problem is formulated as a Hamilton–Jacobi–Bellman equation, solved numerically using a Crank–Nicolson finite difference scheme, and compared with an expected net present value approach under the same economic, biological, and adaptive harvesting assumptions, thereby isolating the effect of the valuation methodology. The results show that both approaches generate similar harvesting policies and population trajectories, with neither suggesting overexploitation over the simulated horizon. Nevertheless, the Real Options framework yields higher project values, primarily due to its treatment of systematic price risk. By linking risk compensation to a spanning asset rather than to an exogenous discount rate, it provides a more internally consistent valuation methodology. The comparison also reveals a trade-off between economic value and biological resilience, as the higher values obtained under the Real Options framework are associated with lower average population levels and greater dispersion in population outcomes. These findings highlight the relevance of Real Options methods for the economic valuation and sustainable management of renewable natural resources under uncertainty.