Fixed point analysis of expectation convergence in financial learning in perturbed metric spaces
Year: 2026
Type: article
Abstract: Financial markets rarely operate under perfect rationality. Price expectations are formed and revised in environments shaped by limited information, behavioral biases, and institutional frictions. In such settings, investors' perceptions of differences between forecasts may deviate from purely rational benchmarks. In this paper, we develop a mathematical framework for expectation updating that captures these perceptual distortions in a perturbed-metric setting. We introduce a new contractive-type learning condition that simultaneously incorporates individual inertia and institutional adjustment frictions. Unlike classical contraction structures, the proposed condition reflects directional interactions and layered perception effects in the updating process. Under a natural stability requirement linking individual and institutional adjustment intensities, we establish the existence and uniqueness of an equilibrium price expectation and prove the convergence of the learning dynamics. Linear and nonlinear specifications illustrate how behavioral and institutional mechanisms jointly determine not only stability but also persistence and the speed of convergence.
Source: AIMS Mathematics
Author: Şeyma Bilazeroğlu
Institution: Çankaya University
Language: English
Topic: Economic theories and models
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: gold
Estimated APC paid: $1,200
OpenAlex ID: W7203530360