Résumé
Sarkar [1] has developed a real option approach for an optimal harvesting of a renewable resource such as fish, when the variation of the stock is govern by a Gaussian process. However, the [1] model does not take into account the occurrence of large and sudden fluctuations that cannot be modeled by the Gaussian white noise, for examples hurricanes, disasters, tsunamis and crashes. Following [1], we think that by adding a Poisson jump component in the stochastic differential equation that govern the variation of the stock, we can find the real option value and the optimal stopping time to harvest . So, this paper derives the optimal fishery harvest policy in a real-option model with a general stochastic logistic growth process with a jump part, harvest-sensitive output price, and both fixed and variable harvesting costs. The policy specifies the harvest trigger and harvest size, while outputs from the model include the value of the fishery and the risk of extinction. We also carry out some sensitivity analysis to see how the optimal policy (and the resulting fishery value and risk of extinction) change when the input parameters are varied, particularly the ecological parameters intrinsic growth rate, volatility of the stock, the intensity and frequency of the jump part of the process and also the economic parameters. If the optimal policy is followed, the risk of extinction will depend on the volatility of the biomass variation and the parameters that characterize the jump part of the stochastic differential equation. In the absence of jump, we have also find the expected value and the variance of the MSY and MEY, and discuss their implications in economic policy for a sustainable harvesting by fisheries.