Optimization of Market Stochastic Dynamics

Author ORCID Identifier

Paramahansa Pramanik:https://orcid.org/0000-0002-7070-5538

Publication Title

Operations Research Forum

E-ISSN

26622556

Document Type

Article

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.

Publication Date

12-1-2020

DOI

10.1007/s43069-020-00028-x

Keywords

Feynman-type path integral, Stochastic control

Department

Department of Mathematical Sciences

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