A stochastic hunting model involving two countries

Abstract

Lei x(t) denote the number of animals of a certain species alive at timer. A stochastic model with nonlinear growth function for the species dynamics is considered. Two countries are exploiting the same stock of animals. The controls that minimize a cost function giving a reward as long as the level of the stock remains between two given constants are found. Moreover, the cost function takes the risk-sensitivity of the optimizers into account. Simulation studies of numerical examples are presented.