A viability analysis for a stock/price model

Abstract

We examine the conditions for the sustainability of a stock/price system based on the use of a marine renewable resource. Instead of studying the environmental and economic interactions in terms of optimal control, we focus on the viability of the system. These viability/crisis situations are defined by a set of economic state constraints. This constraints combine a guaranteed consumption and a minimum income for fishermen. Using the mathematical concept of viability kernel, we reveal that with only economics constraints we guarantee a perennial stock/price system.