Cash Management Using ODE-Based Modeling

Title	Cash Management Using ODE-Based Modeling
Authors	G. _. Zanko¹ ¹Baku State University
Annotation	In this short communication paper a continuous-time model for dynamic corporate cash management is presented, utilizing the principles of optimal control theory. The evolution of a companys liquidity position is formulated through a system of Ordinary Differential Equations (ODEs) that correctly distinguishes between stocks (cash, debt, investments) and flows (rates of borrowing and investment). The problem is framed to minimize financing costs and maximize investment returns over a finite horizon. By applying Pontryagins Maximum Principle, the necessary conditions for optimal financial interventions are derived. The resulting control policies are threshold-based strategies, dynamically guided by the economic shadow prices of cash, debt, and invested capital. This framework provides a financially intuitive and mathematically sound foundation for proactive liquidity management, bridging theoretical control theory with practical corporate finance.
Keywords	ordinary differential equations, cash management, optimal control.
Citation	Zanko G. _. ''Cash Management Using ODE-Based Modeling'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 300-303. Available at: https://conf.svmo.ru/files/2025/papers/paper63.pdf. - Date of access: 30.08.2025.

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Cash Management Using ODE-Based Modeling

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