Joint Stochastic Optimal Control and Stopping in Aquaculture: Finite-Difference and PINN-Based Approaches

Battle Count: 55

The paper's methodology is directly relevant to quantitative trading through its treatment of joint optimal control and stopping problems, which are analogous to portfolio optimization with American options. The HJB variational inequality framework, PINN-based PDE solving, and DeepOS algorithm are all applicable to optimal exercise timing, dynamic hedging, and trading strategy optimization. The stochastic price dynamics modeled as geometric Brownian motions are standard in financial modeling. However, the specific application is aquaculture rather than trading, and the paper does not directly address trading strategies.

The finite difference solver requires careful grid construction, upwind schemes, and GPU parallelization for the 5-dimensional problem. The PINN approach involves training multiple neural networks (value function + control networks), implementing PDE residuals via automatic differentiation, fuzzy boundary sampling, and combining with DeepOS. The training procedure with learning rate schedules, balanced sampling between continuation and stopping regions, and multiple loss components adds complexity. However, the code is publicly available and both methods run in under 10 minutes on a single GPU.

Code and datasets are publicly available on GitHub (https://github.com/kevinkamm/JointOptimalCtrlStopping_Aquaculture). All parameters are explicitly listed in tables. Grid sizes, neural network architectures, training hyperparameters (learning rate schedule, batch size, epochs), and evaluation methodology (8192 Monte Carlo paths) are fully documented. The paper uses a single GPU with 24GB memory.