A Behavioral Perspective on Price Convergence via Perturbed Metric Spaces with An Extended Contraction

Year 2026, Volume: 18 Issue: 1, 32 - 45, 23.02.2026

Şeyma Bilazeroğlu

https://doi.org/10.47000/tjmcs.1761322

https://izlik.org/JA48SY49HU

Abstract

In this study, we examine how investors update their price forecasts over time within a "perturbated metric space," which incorporates behavioral influences and market friction. Classical metric structures are inadequate when the measured distance changes with perceived deviations. Therefore, a new structure is proposed in which the measured distance is modified by perceived deviations. In this context, the existence of a fixed point is guaranteed through an extended contraction inequality, and the convergence behavior of the model is analyzed using different examples. Simulations established under different linear and nonlinear update functions demonstrate that the model can reflect both slow and fast market behaviors that reach equilibrium. The proposed approach mathematically demonstrates that investors can reach a common price expectation in the long run, even with heterogeneous psychological responses.

Keywords

perturbated metric space , fixed point , price convergence

References

• Ciric, L.B., On some fixed point theorems, Publ. Inst. Math. (Beograd) (N.S.), 12(26):19–26, 1974.
• DeGennaro, R. P., Robotti, C., Financial Market Frictions: A Survey, Federal Reserve Bank of Atlanta Economic Review, 92(4) (2007), 1–16.
• Jleli, M., Samet, B., On Banach’s fixed point theoremin perturbed metric spaces, Journal of Applied Analysis and Computation, 15(2) (2025), 993–1001.
• Mas-Colell, A., Whinston, M. D., and Green, J. R., Microeconomic Theory, Oxford University Press, Oxford, 1995.
• Olatinwo, S.O., Some Cˆıri´c-type fixed point results in cone metric spaces, Fixed Point Theory Appl. 2010, Article ID 123094.
• Shiller, R. J., From Efficient Markets Theory to Behavioral Finance, Journal of Economic Perspectives, 17(1) (2003), 83-104.
• Tirole, J., The Theory of Corporate Finance, Princeton University Press, Princeton, 2006.