The Barents Sea contains one of Europe s last large, clean and relatively undisturbed marineecosystems. There are around 150 different fish species in the sea. Among these are some ofthe world s biggest fish stocks. The North-East Arctic cod (NEA), the species we are goingto study in this thesis, is the largest cod stock remaining, accounting for about 50% of thetotal cod catch (ICES 2005), and is one of the main reasons that Norway is the world s thirdlargest exporter of fish, measured by export value.However, the stocks of NEA cod have decreased considerably over the latest decades andare currently at a poor state. At June 2006 ICES (International Council for the Exploration ofthe Sea) issued a far lower recommendation for quotas for NEA cod for 2007. ICESrecommend that the total quota for NEA cod in 2007 should not exceed 309,000 tons adramatic fall from the total quota for 2006 of 471,000 tons. Besides the setting of quotas,regulations aiming at protecting young cod such as minimum catching size and minimummesh size are also adopted.In addition to the serious situation, the NEA cod are now threatened by a new and potentiallydamaging activity oil and gas development. Large amount of unexploited oil reserves arefound in the Lofoten-Barents Sea area. Although there has been no petroleum-exploration inthis area so far, the petroleum industry is eager to get access to these fossil resources.However, harsh climate and short and simple food webs make the marine ecosystem of theBarents Sea particularly sensitive to impacts such as pollution from chemicals and oil. Alarge oil spill would cause dramatic consequences to the marine life in the sea.In this thesis, we focus on the NEA cod, and examine the impact of an oil spill to the codfishery. The problems we are going to study are: What is the optimal fishing strategy How should we change the fishing strategy once there is an oil spill How does the risk of having an oil spill affect the optimal fishing strategy comparedwith the deterministic one?2There have been many literatures concerning the renewable resource management underuncertainty. Clark (P344 349, 1990) argued that the existence of uncertainty had little to dowith the optimal fishing strategy. And a more elaborate mathematical deduction is presentedby Conrad and Clark (1987). But Lewis (1981) used a Markov Decision Process model toanalyze the fishery of the Eastern Pacific yellowfin tuna, and found that there were largedifferences between fishing strategies with deterministic and uncertain conditions. Thedifferences expand with increasing uncertainty. Mirman and Spulber (1985) also examinedthe fishermen s behavior when uncertainty regarding the potential yield exists, but focusedon the effects of landing taxes and vessel quotas. Pindyck (1984) used a risk premium toexamine the effects of fluctuations on resource rent, and found that extraction could increase,decrease, or be left unchanged as uncertainty increased, depending on the extent of market self-correction .The stock growth functions used in the literatures above are total biomass growth functions,but in this thesis we are going to use a more real-life age-structured stock growth model,developed by Hjermann (CEES, 2006), which simulates the recruitment of new cod stockand the growth of cod of each age class. The economic part is the present-value-maximizingfishery model, modeling the economic behavior of a fishery manager. The manager adjustshis harvesting efforts to gain as much profit as possible. The optimal effort path is the onethat maximizes the present value of fishery. This is a discrete time optimization and thealgorithm is known as dynamic programming. The optimization software Premium Solver,which is an extention of the standard Excel Solver developed by Frontline Systems, is usedto compute all the efforts, and shows that pulse fishing is optimal. This specified fishingpattern has been discussed by Clark (P298 301, 1990). The models and results arediscussed in Section 2.In Section 3, we edit our model to a stochastic model, with a stochastic variable entering thestock growth function, representing the risk of having an oil spill. The algorithm ofstochastic optimization is given by Conrad and Clark (P178 188, 1987).If there is an oil spill, cod eggs and larvae bear the major damage. The adult fish can detectpetroleum at very low concentrations and escape from the pollution. But in contrast, fisheggs and larvae are planktonic and exposed to the oil pollution. The laboratory results showthat an oil spill would kill 20% to 25% of cod s eggs and larvae (CEES 2006).3For simplicity, we assume that there are no residuals in the sea after the oil spill, whichmeans we will have new healthy eggs in the next year. After three years, when the damagedgeneration should grow up and enter the fishery, the impact of oil spill would begin toappear when there is less fish to be harvested. As this generation grows closer to the age ofmaximum biomass, the impact would be exaggerated.Our computational results show that harvesting efforts generally decrease when there is aspill, and may even delay as the affected generation reaches the maximum biomass.However, due to discount, the future benefit of reserving more biomass sometimes cannotcompensate the loss of reducing harvesting today, and this leads to the increase of harvestingeffort on the spilling year.Between the deterministic optimal fishing strategy and the strategy under uncertainty, thereare only small differences. In the next part we increase the probability of oil spill to 30/31,and no significant difference is found. Besides the probability of spill, we also change codprice and interest rate. An increase in the price makes harvesting more profitable andincreases all the harvesting efforts. An increase in the interest rate means that future fishresource becomes less important, and more harvesting today is optimal.In the last section, we discuss the inter-species effect briefly, as well as the question ofshould we have oil exploitation in the Barents Sea. The huge benefit from oil exploitation isattractive, but there are still risks of species extinction when an oil spill occurs.