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Book review

Author(s) Gomez M, Guillermo L.
Title Dynamic Probabilistic Models and Social Structure. Essays on Socioeconomic Continuity
Publisher Kluwer Academic Publishers
Year of publication 1992
Reviewed by Dimitar Vandev

The aim of this book is to present an overview on the usage of dynamic stochastic models in the socioeconomic modeling as a part of mathematical economy. It is written in the form of interdisciplinary essays covering a large number of topics, e.g. goal setting, change and time in development and growth processes, stopping times, martingale tuning of driving forces, interacting goals in a variational guise, etc.

The author concentrates on extracting the ideas of modeling out of history of thinking and culture. The statistical and mathematical problems are out of the scope in this book. The main attention is paid to the motivation and relevance of concept of stochastic modeling.

It may be used by anybody wishing to see how the ideas from social sphere are translated into mathematics. It seems however that the book will be especially interesting for probabilists who do not know the various problems of sociometric modeling and are not afraid of the "martingale theory" emphasized in the book. It is extremely useful for experts in mathematical economy helping to enlarge the scope of problems and possible mathematical models to use, as well as for secondary reading for high level students of economy, actuarial and financial mathematics and etc. For the audience, not so sophisticate, the author supplies in the third part a brief presentation of the theory of stochastic differential equations, martingales and stochastic control.

Related topics are treated in a forthcoming book of the author in the same series: Probabilistic Analysis of Disorder and Structural Change: Essays on Socioeconomic Discontinuity.

The book is well written in a good English and the terminology is correctly used. There are many interesting preambles enlightening sections and chapters. There is a good list of references and a index. The book seems too expensive to be personally owned but one can expect that it will be available in most of the libraries of scientific institutions.