Determining the Best Trade-Off Between Expected Economic Return and the Risk of Undesirable Events When Managing a Randomly Varying Population

Abstract

Conditions are given that imply there exist policies that "minimize risk" of undesirable events for stochastic harvesting models. It is shown that for many problems, either such a policy will not exist, or else it is an "extreme" policy that is equally undesirable. Techniques are given to systematically trade-off decreases in the long-run expected return with decreases in the long-run risk. Several numerical examples are given for models of salmon runs, when both population-based risks and harvest-based risks are considered. Key words: Markov decision processes, risk, salmon management, Pareto optimal policies, trade-off curves, linear programing