Necessity of Transversality Conditions for Infinite Horizon Problems

Abstract

This paper studies necessity of transversality conditions for the continuous time, Ž . reduced form model. By generalizing Benveniste and Scheinkman's 1982 ''envelope'' Ž . condition and Michel's 1990 version of the squeezing argument, we show a generaliza-Ž . tion of Michel's 1990, Theorem 1 necessity result that does not assume concavity. The Ž . generalization enables us to generalize Ekeland and Scheinkman's 1986 result as well as to establish a new result that does not require the objective functional to be finite. The new result implies that homogeneity of the return function alone is sufficient for the necessity of the most standard transversality condition. Our results are also applied to a nonstationary version of the one-sector growth model. It is shown that bubbles never arise in an equilibrium asset pricing model with a nonlinear constraint.

The Pontryagin Maximum Principle and Transversality Conditions for a Class of Optimal Control Problems with Infinite Time Horizons

“…There were numerous attempts to find specific situations in which the infinitehorizon Pontryagin maximum principle holds together with additional boundary conditions at infinity (see [12], [15], [16], [21], [26], [31], [36], [38]). However, the major results were established under rather severe assumptions of linearity or full convexity, which made it difficult to apply them to particular meaningful problems (see, e.g., [28] discussing the application of the Pontryagin maximum principle to a particular infinite-horizon optimal control problem).…”

From mind to market: A global, dynamic analysis of R&D

“…13 The necessity of (16), which can be restated as limt→∞ e −ρt Π(c, λ) = 0 and allows exclusion of non-optimal trajectories, was proven by Michel (1982). Kamihigashi (2001) proves the necessity of (17). 14 Observe that in the non-rescaled model, the analogous condition for positive production is that c(t) < A.…”

Limit of the solutions for the finite horizon problems as the optimal solution to the infinite horizon optimization problems

“…dynamical properties of the resultant optimal path have been considered in, for example, Michel (1990), Durán (2000), Kamihigashi (2001), and Le Van and Morhaim (2006).…”