Journal ArticleDOI
A Nonsmooth Approach to Envelope Theorems
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In this paper, a nonsmooth approach to envelope theorems applicable to a broad class of parameterized constrained nonlinear optimization problems that arise typically in economic applications with nonconvexities and/or non-smooth objectives was developed.Abstract:
We develop a nonsmooth approach to envelope theorems applicable to a broad class of parameterized constrained nonlinear optimization problems that arise typically in economic applications with nonconvexities and/or nonsmooth objectives. Our methods emphasize the role of the Strict Mangasarian-Fromowitz Constraint Qualification (SMFCQ), and include envelope theorems for both the convex and nonconvex case, allow for noninterior solutions as well as equality and inequality constraints. We give new sufficient conditions for the value function to be directionally differentiable, as well as continuously differentiable. We apply our results to stochastic growth models with Markov shocks and constrained lattice programming problems.read more
Citations
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Journal ArticleDOI
Envelope theorems in Banach lattices and asset pricing
TL;DR: In this article, envelope theorems for optimization problems in which the value function takes values in a general Banach lattice were developed for optimal discrete-time consumption-portfolio problems with an unrestricted information structure and preferences allowed to display habit formation and state dependency.
ReportDOI
Posterior distribution of nondifferentiable functions
TL;DR: In this paper, the authors examined the asymptotic behavior of the posterior distribution of a possibly non-differentiable function g ( θ ), where θ is a finite-dimensional parameter of either a parametric or semiparametric model.
Journal ArticleDOI
Eliciting time preferences when income and consumption vary: Theory, validation & application to job search
TL;DR: A simple method for eliciting individual time preferences without estimating utility functions even in settings where background consumption changes over time is proposed, which relies on lottery tickets with high rewards.
References
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Book
Optimization and nonsmooth analysis
TL;DR: The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.
Book
Foundations of Economic Analysis
TL;DR: Recent statistical techniques, including nonlinear programming, have been added to a basic survey of equilibrium systems, comparative statistics, consumer behavior theory, and cost and production theory as discussed by the authors, and they have been used in a variety of applications.
Book
Perturbation Analysis of Optimization Problems
TL;DR: It is shown here how the model derived recently in [Bouchut-Boyaval, M3AS (23) 2013] can be modified for flows on rugous topographies varying around an inclined plane.
Book
Supermodularity and Complementarity
TL;DR: In this article, the authors introduce the concept of lattices, supermodular functions, and optimal decision models for cooperative games and non-cooperative games, and present a review of the literature.
Journal ArticleDOI
Envelope Theorems for Arbitrary Choice Sets
Paul Milgrom,Ilya Segal +1 more
TL;DR: The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative as mentioned in this paper.