The Dual Approach to Recursive Optimization: Theory and Examples
开发了一种递归对偶方法，通过拉格朗日函数将动态经济问题与其对偶问题配对，用成本态作为状态变量，简化动态契约和政策问题的求解。
We develop a recursive dual method for solving dynamic economic problems. The method uses a Lagrangian to pair a dynamic recursive economic problem with a dual problem. We show that such dual problems can be recursively decomposed with costates (i.e., Lagrange multipliers on laws of motion) functioning as state variables. In dynamic contracting and policy settings, the method often replaces an endogenous state space of forward†looking utilities with an exogenously given state space of costates. We provide a principle of optimality for dual problems and give conditions under which the dual Bellman operator is a contraction with the optimal dual value function its unique fixed point. We relate economic problems to their duals, address computational issues, and give examples.