Necessity of Transversality Conditions for Stochastic Problems


This paper shows stochastic versions of (i) Michel's (1990, Econometrica 58, 705--723, Theorem 1) necessity result , (ii) a generalization of the TVC results of Weitzman (1973, Manage. Sci.19, 783--789) and Ekeland and Scheinkman (1986, Math. Oper. Res. 11, 216--229), and (iii) Kamihigashi's (2001, Econometrica 69, 995--1012, Theorem 3.4) result, which is useful particularly in the case of homogeneous returns.  These stochastic extensions are established for an extremely general stochastic reduced-form model that assumes neither differentiability nor continuity.

Keywords: Transversality condition
       stochastic optimization
       stochastic reduced-form model
       homogeneous returns
       stochastic growth model

JEL Classification: C61, D90, G12

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