Reverse Calculus and nested optimization

• 成果类型: Article
• 署名作者: Clausen, Andrew; Strub, Carlo
• 署名单位: University of Edinburgh; University of St Gallen
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2020.105019
• 发表日期: 2020
• 关键词: First-order conditions; Non-convex dynamic programming; Stackelberg problems; Unsecured credit

摘要

Nested optimization problems arise when an agent must take into account the effect of their decisions on their own future behaviour, or the behaviour of others. In these problems, calculating marginal costs and benefits involves differentiating the solutions to nested problems. But are these solutions differentiable functions? We develop a tool called Reverse Calculus, and establish first-order conditions for (i) a Stackel-berg leader considering the follower's best response function, (ii) a sovereign borrower considering its own future default policy, and (iii) non-convex dynamic programming problems. (C) 2020 Elsevier Inc. All rights reserved.