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Thread: What does "solved analytically" and "closed-form solution" means?

  1. #1
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    What does "solved analytically" and "closed-form solution" means?

    "Another class of interesting models that typically cannot be solved analytically are
    stochastic dynamic models of rational, forward-looking economic behavior. Dynamic
    economic models typically give rise to functional equations in which the unknown is
    not simply a vector in Euclidean space, but rather an entire function de ned on a
    continuum of points. For example, the Bellman and Euler equations that describe
    dynamic optima are functional equations, as often are the conditions that characterize
    rational expectations and arbitrage pricing market equilibria. Except in a very limited
    number of special cases, these functional equations lack a known closed-form solution,
    even though the solution can be shown theoretically to exist and to be unique."


    What does "solved analytically" and "closed-form solution" means?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by GustavoB View Post
    "Another class of interesting models that typically cannot be solved analytically are
    stochastic dynamic models of rational, forward-looking economic behavior. Dynamic
    economic models typically give rise to functional equations in which the unknown is
    not simply a vector in Euclidean space, but rather an entire function dened on a
    continuum of points. For example, the Bellman and Euler equations that describe
    dynamic optima are functional equations, as often are the conditions that characterize
    rational expectations and arbitrage pricing market equilibria. Except in a very limited
    number of special cases, these functional equations lack a known closed-form solution,
    even though the solution can be shown theoretically to exist and to be unique."


    What does "solved analytically" and "closed-form solution" means?

    Written as a neat finite expression in terms of algebraic and elementary transcendental functions.

    CB
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  3. #3
    MHF Contributor

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    As opposed to numerical approximation or infinite series solutions.
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