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 dynamicalsystem xt+1 = g(xt , zt ), we find a discount factor β* such that for each 0 < β < β* a concaveproblem 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 fractalattractors. 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 Sierpinskicarpet as the unique attractor is provided as an example.
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