Sustainable aquaculture production is influenced by ecological, economic, and environmental uncertainties, yet traditional models often rely on extensive external datasets, making them less applicable in data-scarce regions. This study introduces a Geometric Stochastic Pella-Tomlinson Model that integrates supply elasticity, risk-adjusted economic factors, and environmental variability to optimize aquaculture production in Kenya. By incorporating state-dependent diffusion, the model ensures that stochastic fluctuations scale with production levels, ensuring realistic dynamics, while the Hamilton-Jacobi-Bellman equation is used to derive optimal harvesting strategies under uncertainty. A novel formulation of supply elasticity and its relationship with economic risk using stochastic calculus, along with a risk-sensitive quadratic framework for price elasticity captures market fluctuations. Monte Carlo simulations validate the robustness of the model across varying production conditions, demostrating that higher economic risk correlates with greater supply elasticity, reflecting producers’ responsiveness to price fluctuations in uncertain environments. The model effectively captures declines in aquaculture production due to harvesting pressure, environmental degradation, and market volatility, while price elasticity initially exhibits high sensitivity before stabilizing as risk perception and market responses adapt over time. By aligning with One Health Framework, this approach integrates economic, environmental and ecological factors, providing a data-driven decision-support tool for fisheries managers, to enable risk-aware policy interventions, adaptive production planning, and improved resource allocation. Additionally, by optimizing parameters solely from production data, this framework eliminates reliance on hard-to-access economic datasets while capturing essential economic and ecological interactions. Future research should incorporate real-time economic shock modelling and climate variability to refine the interplay between supply elasticity, market dynamics, and environmental sustainability.
Keywords: Aquaculture production, Economic risk, Supply elasticity, Dynamic optimization, Sustainable fisheries management