Consider an offshore fishing grounds of size K. Suppose the grounds has been overfished to the point that net revenue has been driven to zero and the fishery is in open access equilibrium at (X∞, Y∞). A marine sanctuary, where fishing is prohibited, is then created. Suppose the marine sanctuary is of size K2 and that fishing is allowed on a smaller grounds, now of size K1, where K1 + K2 = K. In the first, deterministic, model, the present value of net revenue from the grounds-sanctuary system is maximized subject to migration (diffusion) of fish from the sanctuary to the grounds. The size of the sanctuary is varied, the system is re-optimized, and the populations levels, harvest, and value of the fishery is compared to the 'no-sanctuary' optimum, and the open access equilibrium. In the deterministic model, a marine sanctuary reduces the present value of the fishery relative to the 'ideal' of optimal management of the original grounds. In the second model net growth is subject to stochastic fluctuation. Simulation demonstrates the ability of a marine sanctuary to reduce the variation in biomass on the fishing grounds. Variance reduction in fishable biomass is examined for different-sized sanctuaries when net growth on the grounds and in the sanctuary fluctuate independently and when they are perfectly correlated. For the stochastic model of this paper, sanctuaries ranging in size from 60 to 40% of the original grounds (0.6 ≥ K2/K ≥ 0.4) had the ability to lower variation in fishable biomass compared to the no sanctuary case. For a sanctuary equal to or greater than 70% of the original grounds (K2 ≥ 0.7K), net revenue would be nonpositive and there would be no incentive to fish.