09 August 2017
Elena Rovenskaya gave a talk on "Early warning signals of regime shifts in time series of data from financial markets".
Optimal harvesting of biological renewable population (such as fish and trees) is one of the classic problems of resource economics. While trying to solve this problem an important question is the level of biological detail and complexity of the chosen model that are sufficient for various purposes. Today exist a range of population models such as exponential population growth, logistic equation as model of population dynamics and recently there has been a growing interest in extending classic fishery models to cover multiple species and metapopulations and to include the age-structure of the population.
In a present work, the age-structured population model described by the linear partial differential equation is considered. This model consists of the evolutionary equation, the boundary condition which is known as fertility equation and the initial condition. The goal is to find the control function that satisfies the model and optimizes several utility functions (economic and ecological utility functions). The presence of several functions is since fishery management handles typically with multiple objectives, in most cases conflicting (maximizing fishing yields, minimizing ecological impacts). In this case we cannot find the optimal solution in a common way. We need to find specific equilibrium solutions.
To solve the problem, we can use the following scheme. First of all it is needed to formulate the problem in a form which is mostly convenient for applying analytical methods. Than it is needed to propose a step-by-step scheme how to find the Pareto frontier. Also, it is needed to propose a difference scheme to solve numerically the dynamic equation. In the method mentioned above can arise next challenges. First of all, it is the possibility to find the analytical solution in dynamic model? How should we value employment, fish stock in the water, etc. What to do if we receive inaccurate input data? Do we need to use in this case specific regularization methods?
Last edited: 21 September 2017
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