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- Title
Fractal steady states in stochastic optimal control models.
- Authors
Montrucchio, Luigi; Privileggi, Fabio
- Abstract
The paper is divided into two parts. We first extend the Boldrin and Montrucchio theorem [5] on the inverse control problem to the Markovian stochastic setting. Given a dynamical system xt+l = g(xt, zt), we find a discount factor ß∗ such that for each 0 « ß « ß∗ a concave problem exists for which the dynamical system is an optimal solution. In the second part, we use the previous result for constructing stochastic optimal control systems having fractal attractors. In order to do this, we rely on some results by Hutchinson on fractals and self-similarities. A neo-classical three-sector stochastic optimal growth exhibiting the Sierpinski carpet as the unique attractor is provided as an example.
- Subjects
STOCHASTIC processes; CASH discounts; CONCAVE functions; FRACTALS; SELF-similar processes; ECONOMIC models
- Publication
Annals of Operations Research, 1999, Vol 88, Issue 1-4, p183
- ISSN
0254-5330
- Publication type
Article
- DOI
10.1023/A:1018978213041