Title
Necessity of Transversality Conditions for Stochastic Problems
Abstract
This paper establishes (i) an extension of Michel's (1990, Theorem
1) necessity result to an abstract reduced-form model, (ii) a
generalization of the results of Weitzman (1973) and Ekeland and
Scheinkman (1986), and (iii) a new result that is useful particularly
in the case of homogeneous returns. These results are shown for
an extremely general discrete-time reduced-form model that does
not assume differentiability, continuity, or concavity, and that
imposes virtually no restriction on the state spaces. The three
results are further extended to a stochastic reduced-form model.
The stochastic extensions are easily accomplished since our deterministic
model is so general that the stochastic model is in fact a special
case of the deterministic model. We apply our stochastic results
to a stochastic reduced-form model with homogeneous returns and
a general type of stochastic growth model with CRRA utility.
Takashi KAMIHIGASHI
Research Institute for Economics and Business Administration
Kobe University
Rokkodai-cho, Nada-ku, Kobe
657-8501 Japan
Phone: (81) 78 803 7036
Fax: (81) 78 803 7059