Robust valuation and optimal harvesting of forestry resources in the presence of catastrophe risk and parameter uncertainty

Paper: arXiv 2502.05340

Authors: Ankush Agarwal, Christian Ewald, Yihan Zou

Abstract

We determine forest lease value and optimal harvesting strategies under model parameter uncertainty within stochastic bio-economic models that account for catastrophe risk. Catastrophic events are modeled as a Poisson point process, with a two-factor stochastic convenience yield model capturing the lumber spot price dynamics. Using lumber futures and US wildfire data, we estimate model parameters through a Kalman filter and maximum likelihood estimation and define the model parameter uncertainty set as the 95% confidence region. We numerically determine the forest lease value under catastrophe risk and parameter uncertainty using reflected backward stochastic differential equations (RBSDEs) and establish conservative and optimistic bounds for lease values and optimal stopping boundaries for harvesting, facilitating Monte Carlo simulations. Numerical experiments further explore how parameter uncertainty, catastrophe intensity, and carbon sequestration impact the lease valuation and harvesting decision. In particular, we explore the costs arising from this form of uncertainty in the form of a reduction of the lease value. These are implicit costs that can be attributed to climate risk and will be emphasized through the importance of forestry resources in the energy transition process. We conclude that in the presence of parameter uncertainty, it is better to lean toward a conservative strategy reflecting, to some extent, the worst case than being overly optimistic. Our results also highlight the critical role of convenience yield in determining optimal harvesting strategies.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical formulation of forest lease valuation under parameter uncertainty using Reflected Backward Stochastic Differential Equations (RBSDEs) and a two-factor convenience yield model. The theoretical framework is well-grounded in empirical data, utilizing Kalman filtering on lumber futures and MLE on US wildfire data. It addresses relevant climate risk and optimal stopping problems with strong clarity and thoroughness.

Research Flowchart

  flowchart TD
    A[Goal: Value Forest Leases & Harvesting Under Uncertainty & Catastrophe Risk] --> B[Data Inputs: US Wildfire Data & Lumber Futures Prices]
    B --> C[Parameter Estimation: Kalman Filter & MLE for Stochastic Convenience Yield]
    C --> D[Model Uncertainty: Define 95% Confidence Region Parameter Set]
    D --> E[Computation: Solve Reflected BSDEs & Run Monte Carlo Simulations]
    E --> F[Findings: Conservative Bounds Mitigate Risk; Convenience Yield Governs Harvesting]

Cited References (65)

1. A real options approach to the valuation of a forestry investment (2002)
2. On solving the multirotational timber harvesting problem with stochastic prices: a linear complementarity formulation (2005)
3. What a difference a stochastic process makes: epidemiological-based real options models of optimal treatment of disease (2018)
4. Optimal timing of salvage harvest in response to a stochastic infestation (2011)
5. The decision to conserve or harvest old-growth forest (1993)
6. The optimal drought index for designing weather index insurance (2021)
7. Climate change, weather insurance design and hedging effectiveness (2012)
8. A stochastic differential equation SIS epidemic model (2011)

1 of 65 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.