  Fishing quotas are unpleasant but efficient to control the productivity of a
fishing site. A popular model has a stochastic differential equation for the
biomass on which a stochastic dynamic programming or a Hamilton-Jacobi-Bellman
algorithm can be used to find the stochastic control -- the fishing quota. We
compare the solutions obtained by dynamic programming against those obtained
with a neural network which preserves the Markov property of the solution. The
method is extended to a similar multi species model to check its robustness in
high dimension.
