Optimization of a Dynamic Profit Function using Euclidean Path Integral

Document pages: 39 pages

Abstract: A Euclidean path integral is used to find an optimal strategy for a firmunder a Walrasian system, Pareto optimality and a non-cooperative feedback NashEquilibrium. We define dynamic optimal strategies and develop a Feynman typepath integration method to capture all non-additive convex strategies. We alsoshow that the method can solve the non-linear case, for exampleMerton-Garman-Hamiltonian system, which the traditional Pontryagin maximumprinciple cannot solve in closed form. Furthermore, under Walrasian system weare able to solve for the optimal strategy under a linear constraint with alinear objective function with respect to strategy.