Feasibility of a fishery regulation model. A pulse quota fishing policy with environmental stochasticity

TL;DR

This paper investigates a fishery regulation model using a stochastic impulsive differential equation with environmental randomness, demonstrating the feasibility of a pulse quota fishing policy under stochastic conditions.

Contribution

It introduces a novel stochastic impulsive model for fishery regulation incorporating environmental variability and proves the finite expectation of access times, ensuring regulation feasibility.

Findings

Finite expected access times are proven, confirming regulation feasibility.

The model incorporates environmental stochasticity via Brownian motion.

Pulse harvesting occurs at random stopping times influenced by environmental effects.

Abstract

An enviromental-random effect over a deterministic population mo\-del, a resource ({\it e.g.}, a fish stock) is introduced. It is assumed that the harvest activity is concentrated at a non predetermined sequence of instants, at which the abundance reaches a certain predetermined level, for then to fall abruptly a constant capture quota (pulse harvesting). So that, the abundance is modeled by a stochastic impulsive type differential equation, incorporating an standard Brownian motion in the per capita rate of growth. With this random effect, the pulse times are images of a random variable, more precisely, they are "stopping-times" of the stochastic process. The proof of the finite expectation of the next access time, {\it i.e.}, the feasibility of the regulation, is the main result.