Harvest control rules have become an important tool in modern fisheries management, and are increasingly adopted to provide continuity in management practices, to deal with uncertainty and ecosystem considerations, and to relieve management decisions from short-term political pressure. We provide the conceptual and institutional background for harvest control rules, a discussion of the structure of fisheries management, and brief introductions to harvest control rules in a selection of present day cases. The cases demonstrate that harvest control rules take different forms in different settings, yet cover only a subset of the full policy space. We conclude with views on harvest control rules in future fisheries management, both in terms of ideal and realistic developments. One major challenge for future fisheries management is closing the gap between ideas and practice.
The economic efficiencies of the Danish, Icelandic, and Norwegian cod fisheries are examined. For this purpose, nonlinear aggregate models of these fisheries are constructed. Comparing the calculated optimal harvest and biomass quantities with the actual fisheries provides a measure of the degree of efficiency in these fisheries. The comparisons confirm that the cod harvesting policies of these countries have been hugely inefficient in the past. It appears that inefficiency has been increasing over the last three to four decades, even after TAC regulations replaced open access, indicating that the management policies adopted by all three countries have failed to cure overfishing.
In this paper we prove a sufficient maximum principle for general stochastic differential Stackelberg games, and apply the theory to continuous time newsvendor problems. In the newsvendor problem a manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits under a random demand rate. Our demand rate is an Itô-Lévy process, and to increase realism information is delayed, e.g., due to production time. We provide complete existence and uniqueness proofs for a series of special cases, including geometric Brownian motion and the Ornstein-Uhlenbeck process, both with time variable coefficients. Moreover, these results are operational because we are able to offer explicit solution formulas. An interesting finding is that more precise information may be a considerable disadvantage for the retailer.
Analytical expressions for optimal harvest of a renewable resource stock which is subject to a stochastic process are found. These expressions give the optimal harvest as an explicit feedback control law. All relations in the model, including the stochastic process, may be arbitrary functions of the state variable (stock). The objective function, however, is at most a quadratic function in the control variable (yield). A quadratic objective function includes the cases of downward sloping demand and increasing marginal costs which are the most common sources for nonlinearities in the economic part of the model. When it is assumed that there is a moratorium on harvest for stock sizes below a certain level (biological barrier), it is shown that the barrier requirements influence the optimal harvest paths throughout. KEY WORDS. Feedback control, renewable resource management, stochastic dynamic optimization.
In this paper, we study how a stochastic model can be used to determine optimal levels of exploitation of the North-East Arctic Cod (NEAC, Gadus morhua). A non-critical depensation growth model is developed for this species in order to examine both deterministic and stochastic cases. Estimation of the biological and the noise term parameters in the stochastic biomass dynamics is based on simulation and use of empirical NEAC data sets for the years 1985–2001. The Kolmogorov– Smirnov criterion-based method is used to estimate both drift and diffusion parameters simultaneously. The estimates turn out to be reasonable and the model is able to capture the salient features of the NEAC dynamics. The model is used to derive optimal levels of exploitation with different diffusion functions in the stochastic case and various discount rates in the deterministic case. Optimal catches are compared to the historical catch records. A striking feature of our modeling results is that these records fit surprisingly well with the infinite discounting tracks, i.e., the bliss solution. Our general results indicate that over fishing has resulted from lack of long-term planning as well as inadequate response to uncertainty. Copyright Springer 2006Kolmogorov–Smirnov statistics, optimal control, parameter estimation, stochastic bioeconomic model, C10, C14, Q20, Q22,
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