Doutoramento em Matemática
Stochastic Differential Equation Harvesting Models: Sustainable Polices and Profit Optimization
Nuno Miguel Baptista Brites

Orientação:  Carlos Alberto dos Santos Braumann

We describe the growth dynamics of a fish or some other harvested population in a random environment using a stochastic differential equation general model, where the harvest term depends on a constant or on a variable fishing effort. We compare the profit obtained by the fishing activity with two types of harvesting policies, one based on variable effort, which is inapplicable, and the other based on a constant effort, which is applicable, sustainable and is socially advantageous. We use real data and consider a logistic and a Gompertz growth models to perform such comparisons. For both optimal policies, profitwise comparisons are also made when considering a logistic-type growth model with weak Allee effects. The mean and variance of the first passage times by a lower and by an upper thresholds are studied and, for a particular threshold value, we estimate the probability density function of the first passage time using the inversion of the Laplace transform.

Keywords: Harvesting Models, Stochastic Differential Equations, Profit Optimization, Sustainable Policies,