A mean-variance approach to fisheries management Marius Radulescu, Constanta Zoie Radulescu, Magdalena Turek Rahoveanu Abstract— A traditional approach for the fish management is the single-species approach. In the last decades a new approach has gained increased recognition. This is the ecosystem-based approach. An approach to fish management that is compatible with the ecosystem-based approach is the portfolio theory. In the present paper we present several mean-variance portfolio selection models for fish management. One of the models is the minimum risk model. For this model we determine the range of variation for the parameter W (that represents a lower limit for the expected return) and for the budget of the harvesting plan. A numerical example for a fish farm of semi-intensive type, located in a village from the Danube Delta, Romania is discussed. An efficient frontier of the minimum risk problem is computed and displayed. Keywords: fisheries management, portfolio theory, mean- variance model, multi-objective programming problem. I. INTRODUCTION traditional approach for the fish management is the single-species approach. Since the 1990s, fisheries managers have been advised to broaden their scope of awareness beyond single-species considerations owing to: - general poor performance of single-species fishery management worldwide. - heightened awareness of interactions among fisheries and ecosystems. - better understanding of the functional value of ecosystems to humans. - recognition of the wide range of societal objectives associated with fishery resources and ecosystems. As a result, fisheries management has been shifting toward an ecosystem-based fisheries management, also called an ecosystem approach to fisheries (EAF). EAF strives to balance diverse societal objectives by taking into account the knowledge and uncertainties of biotic, abiotic, and human components of ecosystems and their interactions and applying an integrated approach to fisheries within ecologically meaningful boundaries. Manuscript received 15 july 2010. This work was supported by the National Center for Program Management under PN II Proiect 1622 (2008 - 2011), Contract: 52123/2008, Management Information System for farms fisheries in the South East Region with implications on the market. M. Radulescu is with the Institute of Mathematical Statistics and Applied Mathematics, Bucharest,ROMANIA(e-mail:mradulescu.csmro@yahoo.com). C. Z. Radulescu is with the National Institute for R&D in Informatics, Bucharest, ROMANIA (e-mail: radulescu@ ici.ro). M. Turek Rahoveanu, is with the Research Institute for Agricultural Economics and Rural Development, Bucharest, ROMANIA (e-mail: mturek2003@yahoo.com). The ecosystem approach to fishery management is a significant step towards sustainable use of the environment. An approach to fish management that is compatible with the ecosystem-based approach is the portfolio theory. A portfolio framework systematically combines fish stocks that are joined by ecology (e.g., predation, competition) and unspecialized fishing technologies (e.g., mixed-species trawls) into a portfolio which balances expected aggregate returns against the risks associated with stock-attribute and other uncertainties. To be productive, however, this framework must be combined with property rights institutions that clearly state management objectives, create long-run time-horizons among harvesters, internalize spillovers caused by ecological and technological jointness, and reduce uncertainty through research and adaptive management. Although the cost of reducing scientific uncertainty about ecological interactions may limit the portfolio approach to intensive management of relatively few species, its scope can be broadened to integrate tradeoffs among more types of marine resources, such as nature preserves and oil and gas deposits. In the present paper we present several mean-variance portfolio selection models for fish management: one multi- objective model with two objective functions and three single objective models (a minimum risk model, a maximum expected return model and an optimal tradeoff model). The minimum risk model is similar to that presented in [1] with the exception of an additional constraint connected to the budget for fish harvesting. Also in our model we determine the range of variation for the parameter W and for the budget of the harvesting plan. A numerical example for a fish farm of semi- intensive type, located in Jurilovca village, Tulcea county, Romania is discussed. An efficient frontier of the minimum risk problem is computed and displayed. II. MATHEMATICAL MODELS APPLIED IN FISHERIES MANAGEMENT Fisheries management is one of the fields where mathematical models of operations research were first used and also where they have been most widely applied. The number of mathematical models in this domain has rapidly grown in the last decades, due to the impressive development of personal computers and commercial software programs. Mathematical programming, differential equations, optimal control, decision theory, neural networks, probability theory, A Proceedings of the International Conference on Applied Computer Science 291