Sustainable Yields in Fisheries: Uncertainty, Risk-Aversion and Mean-Variance Analysis

21 Pages Posted: 28 Sep 2008 Last revised: 16 Apr 2009

See all articles by Christian-Oliver Ewald

Christian-Oliver Ewald

University of Glasgow; Høgskole i Innlandet

Wen-Kai Wang

National University of Kaohsiung - Department of Finance

Date Written: April 15, 2009

Abstract

We consider a model of a fishery in which the dynamic of the unharvested fish population is given by the stochastic logistic growth equation. Similar as in the classical deterministic analogon, we assume that the fishery harvests the fish population following a constant effort strategy. In a first step we derive the effort level that leads to maximum expected sustainable yield, which is understood as the expectation of the equilibrium distribution of the stochastic dynamics. This replaces the non-zero fixed point, in the classical deterministic setup. In a second step, we assume that the fishery is risk averse and that there is a trade off between expected sustainable yield and uncertainty measured in terms of the variance of the equilibrium distribution. We derive the optimal constant effort harvesting strategy for this problem. In a final step, we consider an approach which we call the mean-variance analysis to sustainable fisheries. Similar as in the now classical mean-variance analysis in Finance, going back to Markowitz (1957), we study the problem of maximizing expected sustainable yields under variance constraints, and dual to this, minimizing the variance, e.g. risk, under guaranteed minimum expected sustainable yields. We derive explicit formulas for the optimal fishing effort in all four problem considered and study the effects of uncertainty, risk aversion and mean reversion speed on fishing efforts.

Keywords: Fisheries, Environmental and Resource Economics, Sustainability, Maximum Sustainable Yield, Stochastic dynamic fisheries models

JEL Classification: C73, Q22, Q57

Suggested Citation

Ewald, Christian-Oliver and Wang, Wen-Kai, Sustainable Yields in Fisheries: Uncertainty, Risk-Aversion and Mean-Variance Analysis (April 15, 2009). Available at SSRN: https://ssrn.com/abstract=1274528 or http://dx.doi.org/10.2139/ssrn.1274528

Christian-Oliver Ewald (Contact Author)

University of Glasgow ( email )

Adam Smith Building
Glasgow, Scotland G12 8RT
United Kingdom

Høgskole i Innlandet ( email )

Lillehammer, 2624
Norway

Wen-Kai Wang

National University of Kaohsiung - Department of Finance ( email )

700 Kaohsiung University Rd.
Nanzih District
Kaohsiung 803
Taiwan

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