Rational Expectations Models with Multiplicative Noise

Lianfeng Song (), Hongxia Wang (), Huanshui Zhang () and Hongdan Li ()
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Lianfeng Song: Shandong University of Science and Technology
Hongxia Wang: Shandong University of Science and Technology
Huanshui Zhang: Shandong University of Science and Technology
Hongdan Li: Shandong University of Science and Technology

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 1, No 8, 233-257

Abstract: Abstract This paper is concerned with the multiplicative-noise rational expectations (MRE) problem. By resorting to a linear quadratic optimal control (LQOC) problem, the approximate solution to the MRE problem can be obtained. It is worth highlighting that this approximate solution can be highly close to the exact solution by adjusting weighted matrices in the cost function of the LQOC problem. Since the conditional expectation of the state is involved in the cost function, the LQOC problem is an optimization control with an additional measurability restriction, which is very involved. The orthogonal decomposition technique is used to deal with this measurability restriction. The solvability condition and the optimal decision are given by developing generalized Riccati-type equations. Numerical experiments are provided to illustrate the effectiveness of the achieved results.

Keywords: Rational expectations; Linear quadratic regulation; Orthogonal decomposition; Multiplicative noise (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02275-4

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