Necessity of transversality conditions for stochastic problems

This paper shows stochastic versions of (i) Michel's (Econometrica 58 (1990) 705, Theorem 1) necessity result, (ii) a generalization of the TVC results of Weitzman (Management Sci. 19 (1973) 783) and Ekeland and Scheinkman (Math. Oper. Res. 11 (1986) 216), and (iii) Kamihigashi's (Econometrica 69 (2001) 995, 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.