A Mathematical Model for Enhancing Financial Planning through Behavioral Insights

Abstract

Analyzing financial planning behaviors enhances personal and societal economic stability. This study introduces a mathematical model, rooted in the Theory of Financial Planning Behavior (TFPB), to quantify how behavioral factors influence financial planning and outcomes. Recognizing that traditional economic models often overlook psychological and social influences, we developed a linear model connecting Financial Satisfaction (FS), Financial Socialization (FSo), and Cognitive Factors (CF) to Intention (I), Financial Planning Behavior (FPB), and Financial Outcomes (FO).

Using a Python-based simulation over 20 periods, we tested the model's dynamics, introducing a 25% increase in FSo at period 10 as an intervention. The simulation showed that this intervention increased I, FPB, and FO by 10.2% each, with an elasticity of 0.41.

Scenario analyses revealed that enhancing the translation of I to FPB and FPB to FO yielded greater improvements in FO (28.6% and 25.0%, respectively) compared to adjusting individual factors like FS and FSo (both 20.6%). This highlights the importance of behavioral implementation in achieving better financial outcomes.

This model provides a structured framework for understanding the causal links from behavioral drivers to financial resilience, offering a quantifiable approach to TFPB. Despite its linear simplicity, it serves as a valuable foundation for bridging theory and practice. We recommend future research to validate and calibrate the model empirically, explore non-linear relationships, incorporate dynamic elements, and address individual differences. The model can be used for policy optimization and intervention design to improve financial literacy and promote sound financial behaviors, contributing as an innovative tool for researchers, policymakers, and financial advisors.