Regime switching in a fishery with stochastic stock and price

Abstract

We develop a bioeconomic model of a fishery subject to stock uncertainty and price uncertainty. With a linear control model, the optimal harvest policy is a bang-bang approach to the optimal stock level, where one harvests either at minimum or full capacity. It is assumed that changing the harvest rate is subject to a switching cost. In this case we show that there are two switching curves in stock-price space, one for entering and one for leaving the fishery. Numerical methods are used to characterize the optimal switching policy for the fishery.

Optimal costless extraction rate changes from a non-renewable resource

“…where we have allowed for the case that the growth rate is stochastic (similarly to Nøstbakken, 2006) It is clear that the terms within the supremum are not altered from our original analysis, and thus one might again derive suitable approximations to the optimal extraction rate. However, a subtle distinction is introduced into what constitutes a 'large enough' level of resource.…”

Harvesting in a Fishery with Stochastic Growth and a Mean-Reverting Price

“…Roughgarden and Smith (1996) discuss multiple sources of uncertainty and their potential role in the collapse of fisheries; the focus on collapse has become a staple of later work. More recent articles of particular relevance are Sethi et al (2005), Nøstbakken (2006), Sarkar (2009), andPoudel et al (2013). Sethi et al (2005) study optimal escapement levels in a model that includes uncertainty in growth, stock measurement and policy implementation.…”

“…The result contrasts with the constant escapement level in the deterministic model. Nøstbakken (2006) analyzes policy switching curves in the pricestock space under price and stock uncertainty. When policy switching is costly, entry and exit curves will differ.…”

“…Both Sethi et al (2005) and Nøstbakken (2006) assume a linear objective function. Sarkar (2009), on the other hand, studies a nonlinear objective function and his study is thereby more similar to ours.…”

“…In a real option framework, he finds that the optimal policy has traits similar to pulse fishing regimes that typically arise from linear models. He calculates the optimal harvest trigger (the stock level where it is optimal to exercise the option to harvest); not unlike the entry curve in Nøstbakken (2006). Sarkar (2009) also calculates the optimal harvest size that implicitly defines an exit point in the state space; not unlike the exit curve in Nøstbakken (2006).…”