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Optimization of Market Stochastic Dynamics

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  • Paramahansa Pramanik

    (Northern Illinois University)

Abstract

A Feynman-type path integral has been introduced to find an optimal strategy where a dynamic profit is maximized subject to a stochastic dynamics of a firm’s market share. This method is useful under a more generalized non-linear system such as the Merton-Garman-Hamiltonian process where constructing a Hamiltonian-Jacobi-Bellman equation is very difficult. The path integral method also gives an optimal strategy without going through a value function and gives a different optimal strategy. The result obtained by a Feynman-type method is compared with that by the traditional Pontryagin’s maximum principle.

Suggested Citation

  • Paramahansa Pramanik, 2020. "Optimization of Market Stochastic Dynamics," SN Operations Research Forum, Springer, vol. 1(4), pages 1-17, December.
    • Handle: RePEc:spr:snopef:v:1:y:2020:i:4:d:10.1007_s43069-020-00028-x
    DOI: 10.1007/s43069-020-00028-x
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    References listed on IDEAS

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    1. Chow, Gregory C., 1996. "The lagrange method of optimization with applications to portfolio and investment decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 1-18.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. Ljungqvist, Lars & Sargent, Thomas J., 2012. "Recursive Macroeconomic Theory, Third Edition," MIT Press Books, The MIT Press, edition 3, volume 1, number 0262018748, December.
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    Cited by:

    1. ATM Omor Faruq, 2023. "The Determinants of Foreign Direct Investment (FDI) A Panel Data Analysis for the Emerging Asian Economies," Papers 2307.07037, arXiv.org.
    2. Masud Alam, 2021. "Heterogeneous Responses to the U.S. Narrative Tax Changes: Evidence from the U.S. States," Papers 2107.13678, arXiv.org.
    3. Masud Alam, 2021. "Time Varying Risk in U.S. Housing Sector and Real Estate Investment Trusts Equity Return," Papers 2107.10455, arXiv.org.
    4. Paramahansa Pramanik & Alan M. Polansky, 2024. "Optimization of a dynamic profit function using Euclidean path integral," SN Business & Economics, Springer, vol. 4(1), pages 1-20, January.
    5. Lambert Dong, 2024. "Strategic complementarities as stochastic control under sticky price," Papers 2403.19847, arXiv.org.
    6. Paramahansa Pramanik & Alan M. Polansky, 2023. "Scoring a Goal Optimally in a Soccer Game Under Liouville-Like Quantum Gravity Action," SN Operations Research Forum, Springer, vol. 4(3), pages 1-39, September.

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