Harvesting in a Fishery with Stochastic Growth and a Mean-Reverting Price

Abstract

We analyze a continuous, nonlinear bioeconomic model to demonstrate how stochasticity in the growth of fish stocks affects the optimal exploitation policy when prices are stochastic, mean-reverting and possibly harvest dependent. Optimal exploitation has nonlinear responses to the price signal and should be conservative at low levels of biological stochasticity and aggressive at high levels. Price stochasticity induces conservative exploitation with little or no biological uncertainty, but has no strong effect when the biological uncertainty is larger. We further observe that resource exploitation should be conservative when the price reverts slowly to the mean. Simulations show that, in the long run, both the stock level and the exploitation rate are lower than in the deterministic solution. With a harvest-dependent price, the long-run price is higher in the stochastic system. The price mean reversion rate has no influence on the long-run solutions.

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

“…SDEs have been utilized for describing key elements in renewable energy systems, such as wind speed, solar irradiance forecasting, and water balance in a hydropower reservoir . In addition, SDEs harmonize with the modern mathematical theory of stochastic control, clearly demonstrating that they serve as an appropriate mathematical tool for modeling and control of stochastic system dynamics, as seen in the literature of energy and resource economics . PV systems, which are inherently subject to stochastic weather conditions, would not be an exception.…”

“…28 In addition, SDEs harmonize with the modern mathematical theory of stochastic control, 29 clearly demonstrating that they serve as an appropriate mathematical tool for modeling and control of stochastic system dynamics, as seen in the literature of energy and resource economics. [30][31][32][33] PV systems, which are inherently subject to stochastic weather conditions, would not be an exception.…”

Greed is Good: From Super-Harvest to Recovery in a Stochastic Predator-Prey System

“…with mean zero and variance . The additive noise formulation is a general Wiener process and contains the multiplicative case (Poudel et al, 2015;Kvamsdal et al, 2016). We assume the stock biomass states and harvests to be nonnegative.…”

“…However, most of the economic and biological processes take place in an uncertain environment in reality (Charles & Munro, 1985). Uncertainties in fishery include stock measurement error, parameter estimation errors, environmental variability influencing the growth of fish stocks, structural uncertainty and model error (Charles, 1998;Sethi, Costello, Fisher, Hanemann, & Karp, 2005;Nøstbakken & Conrad, 2007;Roughgarden & Smith, 1996;Poudel, Sandal, & Kvamsdal, 2015;Kvamsdal, Poudel, & Sandal, 2016). Most of the extant literature that evaluates long-term stock management does not consider such uncertainties sufficiently.…”

The Role of Intestinal Microbiota in Chicken Health, Intestinal Physiology and Immunity

“…Fishermen face high financial risk, which is determined by their large annual income fluctuation (Kasperski and Holland, 2013). Moreover, cost fluctuation, alteration of resource user rights, employment loss, and asymmetric market information make market risks more dynamic by influencing the supply of fishery products (Kvamsdal et al, 2016;Sethi, 2010). Some studies divide the fishery risk into natural risk, technical risk, management risk, and market risk.…”