STOCHASTIC

models. In several areas we felt it appropriate to provide new papers that
summarize and extend existing results in the literature. Credit and blame for
biases introduced in the selection of articles and their layout are due to WTZ.
The five parts of this work present material that is intended to be read in a
sequential fashion part by part.
Part I is concerned with mathematical tools and expected utility theory. The
treatment focuses on convexity and the Kuhn-Tucker conditions and the
methods of dynamic programming. The next part is concerned with qualitative
economic results, and particular attention is given to results relating to
stochastic dominance, measures of risk aversion, and portfolio separation
theorems. Part HI is concerned with static models of portfolio selection.
Particular attention is placed on the mean-variance and safety-first approaches
and their extensions along with their relation to the expected utility approach.
The questions of existence and diversifications of optimal portfolio policies
and the effects of taxes on risk taking are also dealt with here. The fourth part
is concerned with dynamic models that are in some sense reducible to static
models. Part V is concerned with dynamic models that are most properly
analyzed by dynamic methods. Particular attention is placed on models of
portfolio revision, optimal capital accumulation, option strategies, and portfolio
problems in continuous time.
Each part begins with an introduction that attempts to summarize and make
cohesive the material that follows. This is followed by several articles that
present major methodological advances in that area. At the end of each part
there are numerous problems which form an integral part of the text and are
subdivided into computational and review, and mind-expanding exercises.
The computational and review exercises are intended to test the understanding
of the preceding readings and how they relate to previous material. Some
exercises present, hopefully, straightforward extensions, to new problems, of
the methodological material in the readings. Other exercises fill gaps in the
presentation of the reprinted articles. The mind-expanding exercises, on the
other hand, are intended to traverse new problem areas whose analysis requires
different techniques or nonstraightforward extensions of the material in the
reprinted articles. Many of these exercises are quite difficult, and some present
unsolved problems and conjectures. We have starred all exercises whose
solution is unknown or in doubt to us. Some mind-expanding exercises describe
previously unpublished problems and solutions. They also serve to survey, to
some extent, many important papers that could not be included because of
space limitations. Indeed, many exercises present major results from one or
more published papers. The sources from which such exercises were adapted
are indicated in the "Exercise Source Notes" at the end of each exercise
section. We have tried to present the exercises in such a way that the reader
can obtain maximum benefit per unit input of time spent in their solution. In
xxxn PREFACE IN 1975 EDITION