STOCHASTIC

technology as in Wallace and Ziemba (2005). The Bradley and Crane model
ushered in a whole literature in bond portfolio management and the management
of fixed income securities; see, for example, the early book of Dempster (1980)
from the first international conference on stochastic programming and the papers
by Mulvey and Zenios (1994), Golub et al. (1995), Zenios et al. (1998) and
Bertocchi and Dupacova in Zenios and Ziemba (2006, 2007) for the current state
of this literature which has moved more to the SP modeling approach using
complex bond pricing which Bradley and Crane initiated in this paper. The
Kusy and Ziemba approach was the first of many aggregated ALM models
which include the Russell-Yasuda model (see Carino and Ziemba, 1998; and
Carino et al, 1994, 1998) and the Siemens Austria pension fund model (see
Geyer et al, 2005) and the several papers on related applications that are
collected in Ziemba and Mulvey (1998), Wallace and Ziemba (2005), the Zenios
and Ziemba ALM Handbook (2006, 2007), and Zenios (2007). A significant
contribution of this line of research, that has been made possible due to the
flexibility of stochastic optimization models to integrate through scenarios
diverse multi-dimensional risk factors, is towards enterprise wide risk management.
Significant improvements in the risk-reward profile of an institution can
be achieved with integrative risk management models using stochastic programming;
see e.g. Babbel and Staking (1991), Consiglio, Cocco and Zenios (2001),
Dempster (2002) and Zenios and Ziemba (2006, 2007).
Section 2 of Part V deals with models of optimal capital accumulation and
portfolio selection. Neave presents conditions for a consumer's multiperiod utility
function to exhibit both decreasing absolute and increasing relative risk
aversion. He shows that these properties are preserved through maximization
and expectation operations over time. Although some generalizations are possible,
Neave essentially solves this problem.
Samuelson and Merton in a pair of companion articles in 1969 devised the
discrete time and continuous time dynamic portfolio consumption-investment
models, respectively, which are used frequently in current research. Merton's
paper and his 1971 paper in Section 4 of Part V are highly related to current
continuous time models such as those described in his book (Merton, 1992)
and in the strategic asset allocation work of Brennan and Schwartz (1998),
Brennan et al. (1997) and Campbell and Viceira (2002), as well as the Black
and Scholes (1973) and Merton (1973) option pricing models. For option
pricing, the continuous time model is essential but for practical asset-liability
modeling the discrete time multiperiod stochastic programming models are more
practical as they allow modeling more of the real constraints and preferences
xx PREFACE AND BRIEF NOTES TO THE 2006 EDITION