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Educación matemática

versão impressa ISSN 1665-5826

Resumo

MARTINEZ PALACIOS, Ma. Teresa V.  e  VENEGAS-MARTINEZ, Francisco. Stochastic optimal control in the teaching of mathematical economics. Educ. mat [online]. 2011, vol.23, n.3, pp. 147-181. ISSN 1665-5826.

In this paper we present in a didactic way the statement of the stochastic optimal control problem in continuous time where constraints are observable diffusion processes driven by the geometric Brownian motion. Furthermore, in order to illustrate the use of stochastic optimal control in Mathematical Economics, we present in an educational way two examples. The first is a model of a rational economic agent that has an initial wealth and faces the decision of how to distribute his wealth in consumption and a portfolio of assets in an infinite planning horizon, so as to maximize his total expected utility for consumption. The second example concerns the case of a finite time horizon of stochastic duration.

Palavras-chave : stochastic dynamic optimization; stochastic optimal control in continuous time; partial differential equation of Hamilton-Jacobi-Bellman; verification theorem of stochastic calculus; n- dimensional Itô's lema.

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