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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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    Cited by:

    1. 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.
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    5. 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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