Optimal management with reversible regime shifts

In this paper we examine the management of a natural resource, a fishery, subject to regime shifting dynamics. A regime shift is defined as an episode in which the dynamics of the resource can switch between two alternative regimes at random times. Specifically, we study the impact of reversible regime switching, both observed and unobserved, on optimal harvesting policy. The case in which the regime is not directly observed, i.e., observational uncertainty, is addressed by using the extended POMDP approach developed in Fackler and Pacifici (2014). We illustrate the performance of the model under different assumptions on the underlying stochastic growth variability, the biological structure of the stock in different regimes, and the resilience of the regimes. When the regime is known optimal policies depend on the population level and which regime is currently active. When the regime is unobserved, on the other hand, the optimal policy depends on the population level and a belief distribution about the current regime. In general when the probability of regime change is fixed, and hence is not affected by harvesting policy, the optimal policy is of the constant-escapement variety. When the probability of switching regime is endogenous the optimal policy is no longer of the constant-escapement type. Optimal policies when the regime is uncertain are approximately equal to a weighted average of the policies when the regime is certain, with the weights equal to the beliefs in the associated regimes, but there are differences.