Reference Points and Optimal Management in Stochastic Age-Structured Fisheries Models

The purpose of this article is to characterize dynamic optimal harvesting trajectories that maximize discounted utility assuming an age-structured population model, in the same line as Tahvonen (2009). The main novelty of our study is that uses as an age-structured population model the standard stochastic cohort framework applied in Virtual Population Analysis for fish stock assessment. This allows us to compare optimal harvesting in a discounted economic context with standard reference points used by fisheries agencies for long term management plans (e.g. Fmsy). Our main findings are the following. First, optimal steady state is characterized and sufficient conditions that guarantees its existence and uniqueness for the general case of n cohorts are shown. It is also proved that the optimal steady state coincides with the traditional target Fmsy when the utility function to be maximized is the yield and the discount rate is zero. Second, an algorithm to calculate the optimal path that easily drives the resource to the steady state is developed. And third, the algorithm is applied to the Northern Stock of hake. Results show that management plans based exclusively on traditional reference targets as Fmsy may drive fishery economic results far from the optimal.