Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and ManagementAn excellent financial research tool, this classic focuses on the methods of solving continuous time problems. The two-part treatment covers closely related approaches to the calculus of variations and optimal control. In the two decades since its initial publication, the text has defined dynamic optimization for courses in economics and management science. Simply, clearly, and succinctly written chapters introduce new developments, expound upon underlying theories, and cite examples. Exercises extend the development of theories, provide working examples, and indicate further uses of the methods. Geared toward management science and economics PhD students in dynamic optimization courses as well as economics professionals, this volume requires a familiarity with microeconomics and nonlinear programming. Extensive appendices provide introductions to calculus optimization and differential equations. |
Contents
Example Solved | 11 |
Solving the Euler Equation in Special Cases | 28 |
Isoperimetric Problem | 43 |
Copyright | |
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a₁ assume boundary conditions c₁ c₂ calculus of variations coefficients concave function constants of integration constraint consumption continuous function continuously differentiable function convex convex function cost curve defined denote discounted dt subject dt to subject dynamic endpoint equilibrium equivalent Euler equation evaluated Example Exercise Figure fixed function x(t FURTHER READING given gives H₁ Hamiltonian Hence holds inequality integrand interval investment jump k₁ k₂ Legendre condition lemma linear differential equation linearly local maximum locus marginal valuation maximize maximum minimizing multiplier nonnegative nonpositive obeyed optimal control optimal path optimal solution partial derivatives particular solution problem production profit r₁ r₂ roots saddlepoint second order Section solve steady stochastic strictly concave subject to x(0 Substituting Suppose t₁ t₂ Taylor's theorem terminal theorem tion transversality condition u₁ w₁ w₂ x(t₁ x(to x₁ zero