## 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. |

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assume boundary conditions calculus of variations capital stock coefficients compute concave function constants of integration constraint consumption continuous function continuously differentiable function control variable convex convex function cost curve defined denote discounted dt subject dynamic dynamic programming endpoint equivalent Euler equation evaluated Example Exercise feasible modifications feedback strategies Figure fixed follows function x(t functions f FURTHER READING given gives Hamiltonian holds Inax increasing inequality infinite horizon integrand interval investment jump Legendre condition lemma linear differential equation locus marginal valuation maximize maximum minimizing multiplier Nash equilibrium nonnegative nonpositive obeyed open-loop optimal path optimal solution order differential equation output parameter partial derivatives particular solution player production profit recall respect right side roots ſ F(t second order Section solve stationary steady stochastic strictly concave subject to x(to Substituting Suppose Taylor series terminal value theorem transversality condition yields zero