Aquaculture

Joint Stochastic Optimal Control and Stopping in Aquaculture: Finite-Difference and PINN-Based Approaches ArXiv ID: 2510.02910 “View on arXiv” Authors: Kevin Kamm Abstract This paper studies a joint stochastic optimal control and stopping (JCtrlOS) problem motivated by aquaculture operations, where the objective is to maximize farm profit through an optimal feeding strategy and harvesting time under stochastic price dynamics. We introduce a simplified aquaculture model capturing essential biological and economic features, distinguishing between biologically optimal and economically optimal feeding strategies. The problem is formulated as a Hamilton-Jacobi-Bellman variational inequality and corresponding free boundary problem. We develop two numerical solution approaches: First, a finite difference scheme that serves as a benchmark, and second, a Physics-Informed Neural Network (PINN)-based method, combined with a deep optimal stopping (DeepOS) algorithm to improve stopping time accuracy. Numerical experiments demonstrate that while finite differences perform well in medium-dimensional settings, the PINN approach achieves comparable accuracy and is more scalable to higher dimensions where grid-based methods become infeasible. The results confirm that jointly optimizing feeding and harvesting decisions outperforms strategies that neglect either control or stopping. ...

On the Impact of Feeding Cost Risk in Aquaculture Valuation and Decision Making ArXiv ID: 2309.02970 “View on arXiv” Authors: Unknown Abstract We study the effect of stochastic feeding costs on animal-based commodities with particular focus on aquaculture. More specifically, we use soybean futures to infer on the stochastic behaviour of salmon feed, which we assume to follow a Schwartz-2-factor model. We compare the decision of harvesting salmon using a decision rule assuming either deterministic or stochastic feeding costs, i.e. including feeding cost risk. We identify cases, where accounting for stochastic feeding costs leads to significant improvements as well as cases where deterministic feeding costs are a good enough proxy. Nevertheless, in all of these cases, the newly derived rules show superior performance, while the additional computational costs are negligible. From a methodological point of view, we demonstrate how to use Deep-Neural-Networks to infer on the decision boundary that determines harvesting or continuation, improving on more classical regression-based and curve-fitting methods. To achieve this we use a deep classifier, which not only improves on previous results but also scales well for higher dimensional problems, and in addition mitigates effects due to model uncertainty, which we identify in this article. effects due to model uncertainty, which we identify in this article. ...