论文标题
使用欧几里得路径积分优化动态利润函数
Optimization of a Dynamic Profit Function using Euclidean Path Integral
论文作者
论文摘要
欧几里得路径积分用于在沃尔拉斯系统，帕累托最优性和非合作反馈纳什平衡下为公司找到最佳策略。我们定义动态的最佳策略，并开发一种Feynman类型路径集成方法来捕获所有非添加凸策略。我们还表明，该方法可以解决非线性案例，例如Merton-Garman-Hamiltonian系统，传统的Pontryagin最大原理无法以封闭形式解决。此外，在Walrasian系统下，我们能够在线性约束下使用线性目标函数在策略方面解决最佳策略。
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.
