Lecture 16

2 Março 2023, 19:00 • Rita Sousa

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Discrete Dynamic Programming with finite horizon vs infinite horizon.

Optimal control in continuous time: formulation of the general optimization problem; Variational approach; the Hamiltonian and the costate variable; necessary and sufficient conditions for a solution; Pontryagin's Maximum Principle; Application.

Lecture 15

2 Março 2023, 17:30 • Rita Sousa

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Dynamic Programming in discrete time: policy function; necessary and sufficient conditions for an optimal solution; Euler equations; transversality condition; Example: Cobb-Douglas optimal growth with log utility; numerical methods based on the contraction mapping theorem.

Lecture 14

28 Fevereiro 2023, 19:00 • Rita Sousa

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Introduction to Dynamic Programming: classification of dynamic programming problems (discrete time vs continuous time, certainty vs uncertainty, finite horizon vs infinite horizon); utility function and discount factor; representative household; optimal growth problem; optimality principle and Bellman's equation.

Lecture 13

28 Fevereiro 2023, 17:30 • Rita Sousa

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Numerical Methods for Ordinary Differential Equations: well-posedness of initial value problems; Euler's method and its error; higher order methods; Runge-Kutta methods (midpoint and 4th order).

Lecture 12

16 Fevereiro 2023, 19:00 • Rita Sousa

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Ordinary Differential Equations: Linear systems of 1st order ODEs; matrix exponential; exercises; qualitative methods for systems of autonomous ODEs; equilibrium points and their stability; Application: predator-prey models.