Individual Growth in a Random Environment: an optimization problem

Abstract

We consider a class of stochastic differential equations model to describe individual growth in a random environment. Applying these models to the weight of mertolengo cattle, we compute the mean profit obtained from selling an animal to the meat market at different ages and, in particular, determine which is the optimal selling age. Using first passage time theory we can characterize the time taken for an animal to achieve a certain weight of market interest for the first time. In particular, expressions for the mean and standard deviation of these times are presented and applied to real data. These last results can be used to determine the optimal selling weight in terms of mean profit.