Stochastic differential equations harvesting models: a real options approach

N. M. Brites, J. Brazão, M. Reis

The sustainable management of renewable natural resources requires decision-making frameworks capable of incorporating bio-economic uncertainty. In this talk, we present a real options framework for optimal harvesting in which both population and market price evolve stochastically. Harvesting is interpreted as an option granting the fisher the right, but not the obligation, to exploit the resource. By constructing a hedged portfolio involving the harvesting option and a spanning asset, we derive a nonlinear HJB PDE describing the value of the harvesting opportunity. As no analytical solution is available, a Crank–Nicolson finite-difference scheme is used to obtain numerical approximations, complemented by Monte Carlo simulations to analyse the stochastic dynamics of the system. Using a Gompertz growth model calibrated with data from the Bangladeshi shrimp fishery, we examine optimal harvesting effort, population dynamics and option value under uncertainty.

Keywords: Stochastic differential equations, Optimal harvesting, Real options, Fisheries management, Monte Carlo simulation

SI: Portuguese Statistical Society invited session in Statistics and Probability
September 2, 2026  11:20 AM
Aula 29

R. Gaio, R. Costa-Miranda, W. González-Manteiga

L. F. Meira Machado

C. Tenreiro