Fuzzy Linear Difference Equations and Ambiguity Propagation in Financial Volatility

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DOI: https://doi.org/10.28924/2291-8639-24-2026-136
Published: Apr 30, 2026
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Tran Trong Huynh, Le Khanh Dang, Le Vu Truong, Fuzzy Linear Difference Equations and Ambiguity Propagation in Financial Volatility, Int. J. Anal. Appl., 24 (2026), 136.

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Tran Trong Huynh, Le Khanh Dang, Le Vu Truong

Abstract

This paper studies a class of fuzzy first-order non-homogeneous linear difference equations under the horizontal membership function (HMF) framework and derives explicit solution representations together with stability and oscillation conditions. Building on these theoretical results, we reinterpret financial volatility persistence through a fuzzy ambiguity perspective. Rather than replacing stochastic volatility models, we provide a complementary interpretation in which volatility clustering corresponds to slow convergence of uncertainty width within a stable fuzzy dynamic system. Using daily data from the Stock Exchange of Thailand (SET), the S&P 500 index, and the VIX over the period 1 January 2010 to 13 March 2026, we examine volatility persistence, shock transmission, and cross-market amplification. The empirical results indicate systematically higher persistence in the emerging market, consistent with slower ambiguity dissipation.

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