Table Of ContentAdvances in Spatial Science
Editorial Board
David F. Batten
Manfred M. Fischer
Geoffrey I.D. Hewings
Peter Nijkamp
Folke Snickars (Coordinating Editor)
Springer-V erlag Berlin Heidelberg GmbH
Titles in the Series
Cristofaro S. Bertuglia, Peter Nijkamp, Gerard Pepping
Manfred M. Fischer and David Banister
and Giorgio Preto (Eds.) Telematics and Transport
Technological Change, Behaviour
Economic Development and Space XII, 227 pages. 1996. ISBN 3-540-60919-9
XVI,354 pages. 1995. ISBN 3-540-59288-1
David F. Batten and Charlie
Harry Coccossis and Karlsson (Eds.)
Peter Nijkamp (Eds.) Infrastructure and the
Overcoming Isolation Complexity of Economic Development
Information and Transportation VIII, 298 pages. 1996. ISBN 3-540-61333-1
Networks in Development
Strategies for Peripheral Areas Tiinu Puu
VIII, 272 pages. 1995. ISBN 3-540-59423-X Mathematical Location and
Land Use Theory
Luc Anselin and IX, 294 pages. 1997. ISBN 3-540-61819-8
RaymondJ.G.M Florax (Eds.)
New Directions in Spatial Yee Leung
Econometrics Intelligent Spatial Decision
XIX,420 pages. 1995. ISBN 3-540-60020-5 Support Systems
XV; 470 pages. 1997. ISBN 3-540-62518-6
Heikki Eskelinen and
Falke Snickars (Eds.) Cristofaro S. Bertuglia,
Competitive European Peripheries Silvana Lombardo and Peter Nijkamp
VIII, 271 pages. 1995. ISBN 3-540-60211-9 Innovative Behaviour in Space
and Time
Jeroen C.J.M. van den Bergh, X, 437 pages. 1997. ISBN 3-540-62542-9
Peter Nijkamp
and Piet Rietveld (Eds.)
Recent Advances in Spatial
Equilibrium Modelling
VIII, 392 pages. 1996. ISBN 3-540-60708-0
Anna Nagumey . Stavros Siokos
Financial Networks
Statics and Dynamics
With 58 Figur~s
and Tables
10
, Springer
Anna Nagumey
University of Massachusetts
SchoolofManagement
Amherst, MA 01003, USA
Stavros Siokos
University of Massachusetts
Department of Mechanical and Industrial Engineering
Amherst, MA 01003, USA
ISBN 978-3-642-63835-0
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Die Deutsche Bibliothek -CIP-Einheitsaufnahme
Nagurney. Anna: Pinancial network : statistics and dynamics; with 10 tables / Anna Nagumey;
Stavros Siokos. -Berlin; Heidelberg; New York; Barcelona; Budapest; Hong Kong; London; Milan;
Paris; Santa Clara; Singapore; Tokyo :
Springer 1997
(Advances in spatial science)
ISBN 978-3-642-63835-0 ISBN 978-3-642-59066-5 (eBook)
DOI 10.1007/978-3-642-59066-5
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Preface
Finance is concerned with the study of capital flows over time and space in the
presence of risk. The existence of distinct sectors in economies, the prolifera
tion of new financial instruments, coupled with the increasing diversification
of portfolios internationally, along with governmental policy interventions, as
well as the presence of transaction costs, have all brought added complexities
to this general problem domain. In this economic and financial environment
there is a clear need for the development and harnessing of appropriate and
rigorous methodological tools, along with computer resources, for financial
and quantitative analyses.
Congruent with the need for analytical and computational tools that are
based on theory and can efficiently handle financial problems of sufficient gen
erality and detail is that the tools also provide added insight into the behavior
and structure of these large-scale, interacting and competitive systems, con
sisting of multiple sectors and multiple financial instruments. Indeed, what
is sought is generality supported by increased clarity.
In this volume we present a theory of multi-sector, multi-instrument fi
nancial systems based on the visualization of such systems as networks con
sisting of nodes and links and the associated flows. Importantly, the depiction
of such problems as networks adds a graphic dimension to the understand
ing of the fundamental underlying economic structure and its evolution over
time. Our framework also depends crucially on the methodologies of finite
dimensional variational inequality theory for the exploration of statics and
equilibrium states and on projected dynamical systems theory for the study
of dynamics and disequilibrium behavior. At the same time, visualization
and formulation of financial problems as network flow problems provide one
with the opportunity of applying network-based algorithms, coupled with the
aforementioned methodologies, for computational purposes.
The recognition of the pivotal role of computational methodologies in fi
nance and their application dates to the early 1950's, beginning with the
seminal work of Markowitz and his contributions to quadratic programming
in the framework of portfolio optimization problems. In fact, the classi-
Vlll Preface
cal mean-variance portfolio optimization problem is a network optimization
problem.
In addition to quadratic programming and, of course, linear program
ming, the field of finance has made use in recent years of such optimization
techniques as nonlinear programming and stochastic programming as well as
network programming and integer programming. Finance has also benefited
from advances in partial differential equations for both modeling and compu
tation purposes. The primary focus in much of the literature, however, has
been on the individual sector or agent and, as such, optimization techniques
are a natural tool since the emphasis is on a single objective function subject
to the appropriate constraints.
Here, in contrast, the topic of concern is the entire financial economy as
an embodiment of the individual sectors in conjunction with their particular
behavior and their interactions over space and time through, for example,
price signals. Consequently, extensions/generalizations of basic optimization
techniques are required, which can elucidate both questions of statics re
volving around the equilibrium state and of the dynamics of the system in
disequilibrium.
Such tools and their application for financial modeling, qualitative anal
ysis, and computation, are the focus of this book.
This book is divided into six major parts, beginning with the introduction
and overview and the economic and finance foundations chapters of Part I,
and ending with the empirical analysis chapter of Part VI. The book contains
fifteen chapters, with a Sources and Notes section concluding each chapter,
along with references.
Part I provides the background and context for the book in terms of
economics and basic finance. Part II lays the methodological foundations of
finite-dimensional variational inequality and optimization theory, projected
dynamical systems theory, and network theory at a level that is utilized in
Parts III, IV, and V. Parts III and IV develop the financial models, along
with their qualitative properties, and provide algorithms for their solution,
with numerical examples for illustrative purposes. Part V discusses flow of
funds accounts and their network structure whereas Part VI concludes this
volume with a discussion of empirical analysis.
In particular, in Part II we demonstrate how the mathematical tools can
be utilized for both qualitative analysis and computational purposes. The
presentation therein is such that the reader can familiarize oneself with these
topics at first reading and can delve more deeply through additional citations,
depending on one's needs and interests.
In Part III, single country, multi-sector, multi-instrument financial mod
els are developed, beginning with perfect market models (in the absence of
transaction costs and policy interventions). We present first static models, fo
cusing on the variational inequality formulations of the governing equilibrium
conditions, and then derive their dynamic counterparts. In these models, not
Preface IX
only are the optimal composition of assets and liabilities for each sector deter
mined, but also the equilibrium instrument prices. We also discuss extensions
to the basic financial equilibrium models that incorporate such features as
futures and options in order to model the possibility of hedging. We iden
tify the network structure(s) out of equilibrium as well as in equilibrium and
demonstrate how the network structure can be exploited for computational
purposes.
Subsequently, we consider the case of imperfect markets in which the sec
tors are subjected to transaction costs and policy interventions in the form
of taxes and price bounds, i. e., price floors and ceilings. We derive the new
equilibrium conditions along with the variational inequality formulations and
discuss the effects on the financial networks of such market imperfections. Fi
nally, we study dynamic counterparts of these models both from a qualitative
perspective as well as computationally.
In Part IV, we turn to international finance and present multi-country,
multi-sector, multi-currency, multi-instrument financial models in which not
only is the optimal composition of assets and liabilities for each sector deter
mined, but also the instrument prices in terms of a basic currency, as well as
the exchange rates. This part, hence, adds an international dimension to the
single country (and single currency) models of Part III. Again, we begin with
the perfect market assumption and consider both static and dynamic models.
Subsequently, we relax this assumption in order to treat taxes, transaction
costs, and price bounds. In this part, unlike in Part III, the static and dy
namic models are developed within the same chapters, in order to see the
synthesis immediately.
Part V focuses on flow of funds accounts and their estimation as the
solution of optimization problems and identifies and exploits the network
structure of this general equilibrium system. Therein the accounts are related
to the financial models in Part III.
Finally, Part VI provides an accompaniment to the theoretical founda
tions of financial networks through discussions of empirical analysis.
The financial network framework developed here captures the essential
components of the economic structure of financial macro systems in both a
visual medium and mathematically and can be utilized for modeling, analysis,
and computation purposes.
The intended audience for this book includes students, researchers, and
practitioners in finance, in computational economics, and in operations re
search and management science, who are interested in the formulation, qual
itative analysis, and computation of financial equilibrium problems in both
static and dynamic settings.
The writing of this book was made possible, in part, by the sponsorship
of the Royal Institute of Technology (KTH) in Stockholm, Sweden, while the
first author was a Distinguished Guest Professor there in 1996. The support
of Dr. Janne Carlsson, President of KTH and Dr. Ingmar Grenthe, Vice
x Preface
President of KTH, is acknowledged. The hospitality of the host institution
and, in particular, the Divisions of Regional Planning and Optimization and
Systems Theory at KTH are warmly appreciated. The support of Swedish
academic colleagues, notably, Professor Folke Snickars of the Department of
Infrastructure and Planning, Division of Regional Planning, Professor An
ders Lindqvist of the Department of Mathematics, Division of Optimization
and SysteIl!-.s Theory, and Professor Borje Johansson of Regional Planning at
KTH and Enkoping University in this endeavor is also recognized as is the
support of Dr. Ake Andersson, Director of the Institute of Future Studies
in Stockholm. The friendship and hospitality of Dr. Anders Forsgren and
Dr. Xioaming Hu of the Division of Optimization and Systems Theory at
KTH as well as Lars Lindqvist of Regional Planning at KTH are appreciated.
The first author acknowledges helpful conversations with Professor David E.
Boyce of the University of Illinois at Chicago who spent part of his sabbatical
leave at KTH as a Guest Professor of Regional Planning. The presence and
wisdom of Professor Martin Beckmann of Brown University, an intellectual
godfather, are also acknowledged.
The research described herein was supported, in addition, in part, by
a National Science Foundation Faculty Award for Women, NSF Grant No.
DMS-9024071 and by an earlier grant from the Economic Research Service
of the United States Department of Agriculture.
The resources of the Illinois National Center for Supercomputer Appli
cations at the University of Illinois at Urbana, Illinois and at the Cornell
Theory Center at Cornell University in Ithaca, New York were utilized for
the computational work.
We are grateful to our families and collaborators and, in particular, to Dr.
Sten Thore, formerly of the IC2 Institute at the University of Texas at Austin
and to Professors Ding Zhang and June Dong of the State University of New
York at Oswego, without whom this book would not have been possible. We
also acknowledge the support of Professor Richard Giglio of the Department
of Mechanical and Industrial Engineering at the University of Massachusetts
at Amherst.
Finally, we would like to thank Dean Tom 0 'Brien of the School of Man
agement, Professor Nelson Lacey, Chair of the Department of Finance and
Operations Management at the University of Massachusetts at Amherst, and
Professor Ben Branch, as well as Professor Thomas Schneeweis, Director, and
Professor Hossein Kazemi, Associate Director, of the Center for International
Security and Derivative Markets at the School of Management at the Uni
versity of Massachusetts at Amherst for their collegiality and support in our
research endeavors.
Contents
Preface Vll
I Background 1
1 Introduction and Overview 3
1.1 Sources and Notes . . . . 11
2 Foundations of Financial Economics 15
2.1 Historic Overview ......... . 16
2.2 Utility Theory and Risk Aversion. 24
2.3 Market Equilibrium ...... .. 30
2.4 International Financial Economics 34
2.5 Sources and Notes ........ . 39
II Methodological Foundations 47
3 Variational Inequalities 49
3.1 The Variational Inequality Problem. 50
3.2 Qualitative Properties .. . 59
3.3 Algorithms ...... . ...... . 64
3.3.1 Projection Methods .... . 66
3.3.2 Basic Decomposition Algorithms 67
3.4 Sources and Notes .. . . . . . . . . .. 70
4 Projected Dynamical Systems 74
4.1 A Projected Dynamical System 75
4.2 Stability Analysis. 82
4.3 Algorithms ... . 85
4.4 Sources and Notes 89
