Finite Approximations in Discrete-Time Stochastic Control by Naci Saldi Tamás Linder & Serdar Yüksel

Author:Naci Saldi, Tamás Linder & Serdar Yüksel
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

4.6.2 Fisheries Management Problem

In this example we consider the population growth model, called a Ricker model (see [68, Section 1.3]), given by

(4.42)

where , X t is the fish population size in season t, and A t is the population to be left for spawning for the next season, or in other words, X t  − A t is the amount of fish captured in the season t. The one-stage “reward” function is u(x − a), where u is some utility function. In this model, the goal is to maximize the average reward.

The state and action spaces are , for some . Since the population left for spawning cannot be greater than the total population, for each x ∈X, the set of admissible actions is which is not consistent with our assumptions. However, we can (equivalently) reformulate the above problem so that the admissible actions A(x) will become A for all x ∈X. In this case, instead of dynamics in equation (4.42) we have

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