研究報告書

Value Functions and Transversality Conditions for Infinite-Horizon Optimal Control Problems

eng

比較経済研究所ワーキングペーパー

143

1

35

2008-12-18

Version of Record

逐次的効用関数・曖昧さ・時間不整合性を考慮した国際マクロ分析;3

This paper investigates the relationship between the maximum principle with an infinite horizon and dynamic programming and sheds new light upon the role of the transversality condition at infinity as necessary and sufficient conditions for optimality with or without convexity assumptions. We first derive the nonsmooth maximum principle and the adjoint inclusion for the value function as necessary conditions for optimality that exhibit the relationship between the maximum principle and dynamic programming. We then present sufficiency theorems that are consistent with the strengthened maximum principle, employing the adjoint inequalities for the Hamiltonian and the value function. Synthesizing these results, necessary and sufficient conditions for optimality are provided for the convex case. In particular, the role of the transversality conditions at infinity is clarified.

Working Paper