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Deterministic risk modelling: Newtonian dynamics in capital flow

Author

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  • Szczypińska, Anna
  • Piotrowski, Edward W.
  • Makowski, Marcin

Abstract

Risk is a universal concept that is applied in many scientific disciplines. We demonstrate the relationship between the risk associated with the dynamics of capital flows and a specific class of problems from classical mechanics, which rely solely on the deterministic nature of the constructed models. This approach differs from the currently dominant one, where risk is mainly associated with probabilistic methods of modelling Brownian motion. We point out the safest form of loan repayment while considering profit maximization. We derive formulas that allow us to calculate the value of capital at any discrete moments in time, given lower and upper interest rate bounds. We use matrix rates and Newton’s principles to analyse capital dynamics in both continuous and discrete systems. We illustrate the proposed theory with a practical example: a measure of the efficiency of buying and selling transactions.

Suggested Citation

  • Szczypińska, Anna & Piotrowski, Edward W. & Makowski, Marcin, 2025. "Deterministic risk modelling: Newtonian dynamics in capital flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 665(C).
    • Handle: RePEc:eee:phsmap:v:665:y:2025:i:c:s0378437125001517
    DOI: 10.1016/j.physa.2025.130499
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    References listed on IDEAS

    as
    1. Makowski, Marcin & Piotrowski, Edward W. & Sładkowski, Jan, 2019. "Schrödinger type equation for subjective identification of supply and demand," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 131-137.
    2. Zambrzycka, Anna & Piotrowski, Edward W., 2007. "The matrix rate of return," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 347-353.
    3. Piotrowski, Edward W. & Sładkowski, Jan & Syska, Jacek, 2010. "Subjective modelling of supply and demand—the minimum of Fisher information solution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4904-4912.
    4. Makowski, Marcin & Piotrowski, Edward W. & Sładkowski, Jan & Syska, Jacek, 2017. "Profit intensity and cases of non-compliance with the law of demand/supply," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 53-59.
    5. E. W. Piotrowski & M. Schroeder, 2007. "Kelly criterion revisited: optimal bets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 201-203, May.
    6. Piotrowski, E.W. & Sładkowski, J., 2003. "The merchandising mathematician model: profit intensities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(3), pages 496-504.
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