Optimization of a Dynamic Profit Function using Euclidean Path Integral
Theoretical Economics
2020-02-24 v1 Optimization and Control
Probability
Abstract
A Euclidean path integral is used to find an optimal strategy for a firm under a Walrasian system, Pareto optimality and a non-cooperative feedback Nash Equilibrium. We define dynamic optimal strategies and develop a Feynman type path integration method to capture all non-additive convex strategies. We also show that the method can solve the non-linear case, for example Merton-Garman-Hamiltonian system, which the traditional Pontryagin maximum principle cannot solve in closed form. Furthermore, under Walrasian system we are able to solve for the optimal strategy under a linear constraint with a linear objective function with respect to strategy.
Cite
@article{arxiv.2002.09394,
title = {Optimization of a Dynamic Profit Function using Euclidean Path Integral},
author = {P. Pramanik and A. M. Polansky},
journal= {arXiv preprint arXiv:2002.09394},
year = {2020}
}