The Mathematics Behind Financial Decision-Making: How Quantitative Models Shape and Misshape Investor Behavior

Abstract

Financial markets are widely assumed to operate on logic and data. Yet the decisions made within them — by professionals and retail investors alike, consistently deviate from what models predict. This paper examines the mathematical infrastructure underlying modern finance, the structural gap between theoretical models and real-world application, and the behavioral patterns that emerge when that gap is ignored. The research draws on primary interviews conducted with academics and finance professionals from institutions including CUNEF Universidad (Madrid), Lincoln University, Universitat Pompeu Fabra (Barcelona), and the Gulf University for Science and Technology, as well as a review of existing literature on quantitative finance, behavioral economics, and market efficiency. Key findings suggest that mathematical models in finance are approximations that perform well under stable conditions and fail predictably under stress. The Efficient Market Hypothesis, while theoretically robust, is routinely violated by investor behavior driven by overconfidence, speculative assumptions, and information asymmetry. Furthermore, the emergence of AI and machine learning introduces powerful predictive capability but creates a new tension between accuracy and interpretability — a tension with significant implications for financial regulation and systemic risk. The paper concludes that financial literacy, at both individual and institutional levels, must move beyond familiarity with instruments and toward a deeper understanding of the assumptions embedded in the models that price them. Future research directions include the mathematical modeling of Islamic finance risk-sharing structures and the application of network theory to financial contagion.

Keywords

Convergence Science - Social Science

Citation

Publication Details

License: Author-retained; open access display by NSRI unless a separate article license states otherwise.

Peer review status: Editorial and integrity screening for archive display; archive placement does not imply formal journal publication by NSRI.

AI disclosure: No AI disclosure is attached to this public record unless stated in the manuscript.

Conflict of interest statement: No conflict of interest statement is attached to this public record unless stated in the manuscript.

References

References are available in the manuscript PDF when provided.