STOCHASTIC

using or others could use this book in courses, seminars and workshops that deal
with useful theory for real investment problems.
The 1975 edition was used by many students and faculty and helped evolve
the then young field of optimization under uncertainty models of theory and
economic results. Part I on mathematical tools focuses on expected utility
theory, convexity and the Kuhn-Tucker conditions and dynamic programming.
Each of these areas was well developed in 1975; however, progress has
continued in all three areas. Fishburn's comprehensive theory of subjective
probabilities and expected utilities still provides an excellent introduction to
utility theory. A notable subsequent area of expected utility theory is the prospect
theory of Kahneman and Tversky (1979, 1982), work for which Kahneman
won the Nobel prize in economics in 2003. They devised a utility theory to
analyze the notion that individuals typically fear loss greater than they enjoy
gains, that there is framing of decisions with different decisions made in identical
situations except the way it is presented and that low probability events are
typically overestimated and high probability events underestimated. These ideas
are used in many places in mainstream academic finance, financial engineering,
fund management and other areas, and some date from much earlier. For
example, articles on the favorite-longshot bias, related to the third Kahneman
and Tversky area, were originally published in 1949 and 1956. They are
reprinted in the racetrack efficiency studies volume of Hausch, Lo and Ziemba
(1994). The bias there is that high probability events have somewhat higher
expected average returns and low probability events are greatly overestimated.
The advent of betting exchanges such as Betfair and rebate betting has flattened
this bias somewhat but it is still strong; see Hausch and Ziemba (2007). Hausch,
Ziemba and Rubinstein (1981) introduced the notion that biases might be
exploitable in racetrack betting if you use probabilities from simple markets in
complex markets. That paper and Hausch and Ziemba (1985) introduced Kelly
log utility betting into racetrack betting models. This area has grown immensely
as well and a recent survey with updated results is in Hausch and Ziemba
(2007). Tompkins, Ziemba and Hodges (2003) show that biases are similar in
the S&P500 and the FTSEIOO stock indices as well. The two papers by
Mangasarian on pseudo-convex and composite functions remain classics to this
day and are constantly used in portfolio theory by those who know about them.
Dynamic programming remains an active field and it is frequently used in
economic and financial studies. My (Ziemba) paper is still a useful introduction
to the theory and concepts. See Bertsekas (2005) for a through treatment, in
discrete and continuous time. Campbell and Viceira (2002) is a recent example
XIV PREFACE AND BRIEF NOTES TO THE 2006 EDITION