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YLE13: Optimal control theory

Delve into optimal control theory methods for maximizing economic benefits from natural resources while ensuring long-term sustainability. Understand the principles, equations, and necessary conditions through dynamic optimization and numerical modeling courses.

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YLE13: Optimal control theory

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  1. YLE13: Optimal control theory Marko Lindroos

  2. Courses after • Dynamic optimisation • Licentiate course • Numerical modeling course

  3. Journals • Natural Resource Modeling • Marine Resource Economics • Journal of Bioeconomics • Resource and Energy Economics

  4. Conferences • Resource Modeling Association • IIFET • EAFE

  5. Assumptions • state of the natural resource changes in time (deterministic) • objective is to optimise the use of the resource in the long-run • state of the resource is a constraint in the economic optimisation problem

  6. Optimal control • Optimalcontrolproblem: How to choosethecontrol to maximiseeconomicbenefitsfromtheresource • Optimalcontrolresults in an optimaltimetrajectory of thestate

  7. • We can define optimal use of natural resource for future years and the following resource stock level • If we deviate from the optimal control at any point in time the economic benefits (Net Present Value) will decrease

  8. Present value maximum principle • Equation of motion for resource x: • Differential equation where state variable is x, control variable is u (for non-renewable we denote the control with q and renewable with h)

  9. Initial and terminal stated • Initial state x(0) known • Terminal state x(T) is zero with non-renewable resources (in our Hotelling model)

  10. Objective function • Max • St equation of motion, initial state, terminal state

  11. Hamiltonian • Here lambda is the costate variable. (Note that Lagrangian in static optimisation is very similar).

  12. Hamiltonian measures: • Instant benefits+ future benefits

  13. Necessary conditions of the maximum principle 1. Optimal control 2. Dynamic condition 3. Equation of motion

  14. Current value Hamiltonian • Myy = current value costate variable

  15. Current value maximum principle • Dynamic condition changes:

  16. Maximum principle (current value) 1. Optimal control 2. Dynamic condition 3. Equation of motion

  17. Projects • BIREGAME, game theory, valuation, Baltic Sea Fisheries (Univ Algarve, Univ Southern Denmark, Imperial College London, VATT) • ECA, Economics of Aquatic foodwebs (VATT, SYKE, LUKE) • NORMER, Climate change effects on marine ecosystems and natural resource economics (Univ Oslo coordinates)

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