Complexity Science: an introduction (and invitation) for actuaries

220 Pages·2010·7.58 MB·English

by  Alan Mills

Health
SOCIETY OF ACTUARIES Section

Complexity Science

An introduction (and invitation) for actuaries

Prepared by
Alan Mills FSA ND

Version 1
June 10, 2010

The opinions expressed and conclusions reached by the author are his own and do not represent any official position or opinion of
the Society of Actuaries or its members. The Society of Actuaries makes no representation or warranty to the accuracy of the
information.

©2010 Society of Actuaries. All rights reserved.
Complexity science – an introduction (and invitation) for actuaries

The greatest challenge today, not just in cell biology and ecology, but in all of
science, is the accurate and complete description of complex systems.
Edward O. Wilson, 1990

The central task of theoretical physics in our time is no longer to write down the
ultimate equations but rather to catalogue and understand emergent behavior in
its many guises, including potentially, life itself. We call this physics of the next
century the study of complex adaptive matter … We are now witnessing a
transition from the science of the past, so intimately linked to reductionism, to the
study of complex adaptive matter … with its hope for providing a jumping-off
point for new discoveries, new concepts, and new wisdom.
Robert Laughlin and David Pines, 2000

I think the next century will be the century of complexity.
Stephen Hawking, 2000

Cover page: Gene ontology network (see Chapter four).
Complexity science – an introduction (and invitation) for actuaries
CONTENTS

Acknowledgments
Introduction 1
PART I A NEW SCIENCE
ONE Complexity Science 6
Science of the real world
TWO Agent-based models 28
The heart of Complexity Science
PART II COMPLEXITY SCIENCE MODELS
THREE Four archetypal models 49
The four archetypal models of Complexity Science
FOUR Networks 53
Agents and relationships
FIVE Cellular automata 77
Agents, relationships, and behavior rules
SIX Artificial societies 119
Agents, relationships, behavior rules, and an environment
SEVEN Serious games 156
Agents, relationships, behavior rules, an environment, and a player

PART III AN INVITATION
EIGHT The complex systems actuary 172
Vision for a new type of actuary
NINE Next steps 178
Steps to develop complex systems actuaries

Top ten Complexity Science books
Essential resources
Finding the essential resources
Glossary

CONTENTS
Complexity science – an introduction (and invitation) for actuaries
ACKNOWLEDGMENTS
I am grateful to many for their encouragement, advice, and support:

 During my Complexity Science presentation at the 2009 Health Spring Meeting, Judy Strachan
recognized how important this subject could be for actuaries, and afterwards encouraged me to
write about it for the Society of Actuaries (SOA). Judy helped obtain funding for this report, and
chaired the report’s Project Oversight Group.

 After considering Judy’s invitation, I initially doubted that many actuaries would see the potential
of Complexity Science, and so initially declined to write about it for actuaries. Steve Siegel
persuaded me to reconsider. He argued convincingly that many actuaries would welcome the
insights and tools of Complexity Science to help them solve the ever-more complex problems they
face.

 During the report’s preparation, members of its Project Oversight Group gave consistently wise
counsel, engaged support, and helpful critique. The members are:
– July Strachan, Chair
– Steve Conwill
– Syed Mehmud
– Bernie Rabinowitz
– Lee Smith
– John Stark
– Steve Siegel, SOA Research Actuary
– Sara Teppema, SOA Staff Fellow for Health
– Barbara Scott, SOA Research Administrator

 Dave Snell – a fellow Complexity Science aficionado, experienced editor, and actuary – offered
sound suggestions for improvement.

 Scott Page, a prominent Complexity Science expert, provided many detailed and helpful
recommendations to improve the report.

 Randall Rupper, a full-time physician and part-time Complexity Science researcher, suggested
several improvements.

 Neil Cantle, Tom Conway, Rick Gorvett, Don Mango, Jon Palin, and Michael
Shumrak are actuaries who are Complexity Science pioneers. They shared their related
experiences and contacts, and enthusiastically supported this report.

 Lisa Canar, my wife, read every word of the report and every line of computer code – many
times – and offered helpful suggestions each time. Even more difficult to achieve, she and our small
children, Calun and Ariana, stayed consistently supportive during the many evenings and nights
of my absence while I wrote this report.

To all of you, my warmest thanks.

ACKNOWLEDGMENTS
Complexity science – an introduction (and invitation) for actuaries
INTRODUCTION
A. MORE THAN AN INTRODUCTION
Complexity Science is a new way to grasp and manage reality.
Not the simple reality of planetary motion and gambling dice that My affair with complexity

has been the study of traditional science. But the complex reality
It was the summer of 2005 when, finally, I saw a
in which we live: the world of hurricanes and earthquakes, social
gleam of hope that the US healthcare system can
reforms and economic upheavals, interest rate fluctuations, be understood. That summer I worked with the
business cycles, and healthcare expenditure trends. In this report, Center for the Study of Complex Systems at the
I will introduce you to this surprising and useful new science. University of Michigan in Ann Arbor, and I read
Joshua Epstein and Robert Axtell’s potent little

book Growing artificial societies.1
But this report is more than an introduction. In it, I will also make

an argument, and extend an invitation to you. At least ten years before, I knew the US
healthcare system was in trouble, but I could
I will argue that today’s complex world demands a new breed of not understand why. As a healthcare consumer,
actuary, and physician, I had experienced many
actuary, a professional I call a ‘complex systems actuary’, who:
sides of the healthcare problem: the lack of
 Understands the complex nature of social systems. coverage, runaway expenditures, and tortuous
reimbursement procedures.
The social systems in which actuaries work (the worlds of

insurance, pensions, investments, and health care) are not
After studying the problem and divers analyses
well-behaved like planets and dice. Rather, they are complex of it, I came to a shocking realization: even
and unpredictable. though nearly everyone offered fixes for the
 Applies new methods. Traditional actuarial methods alone healthcare system, no one understood it.

cannot model complex social systems. To grasp and manage
I assumed that the system was too complex to
the systems in which we work, we must augment our tools
be understood, and that healthcare policy would
with the new methods of Complexity Science. forever be gropings of the blind. But then, in
 Expands the role of actuaries. Actuaries need not be 2003, I read Stephen Wolfram’s newly
published book A new kind of science.2 It was
merely administrators within society’s problem-prone
unlike anything I had seen, a brilliant light that
systems. Rather, we also can use our unique knowledge and
led me to Ann Arbor to learn about Complexity
skill, augmented with insights and tools from Complexity Science. There, while reading Epstein and
Science, to help solve society’s great problems and improve Axtell’s book, I saw that the healthcare system
our social systems. can be modeled and understood, that clear-
sighted healthcare policy is possible.

I will invite you to become such an actuary. No matter if you are a
Since then, I have also learned that all the
veteran or just starting out, you can learn to use the insights and complex social systems in which actuaries work
tools of Complexity Science to address the most pressing can be modeled and understood, but that for
problems of your employer, your clients, and society as a whole. this purpose traditional actuarial methods are
insufficient.
Your fitness for our complex world may depend on whether you

accept this invitation, or simply send regrets.
In this report, I will share with you what I have
learned.

1 Epstein & Axtell (1996), one of this report’s Top ten Complexity Science books.
2 Wolfram (2002), also one of this report’s Top ten Complexity Science books.
INTRODUCTION 1
Complexity science – an introduction (and invitation) for actuaries
B. MAJOR THEMES
Throughout this report I interweave five themes:

1. Social systems are complex systems. The social systems
in which actuaries work are complex systems, with
mechanisms dramatically different from those of simple
systems such as planets and dice. To understand and manage
the behaviors of such systems – this is society’s greatest
challenge.

2. We must study complex system behavior from the
bottom up. The behavior of a complex system arises from
the bottom-up, from its components, the relationships among
its components, and the behavior rules that the components
follow. To understand and manage such systems, we must
model them from the bottom up, using special methods of
Complexity Science, rather than top-down traditional
actuarial methods.

3. Long-term prediction of complex systems is
impossible. The long-term behavior of complex systems –
such as the fluctuations of financial market prices and health
care trend rates – cannot be accurately predicted for more
than short periods. Actuaries pursuing long-term prediction
of complex systems are wasting time.

4. Understanding and effectively managing complex
systems is possible. Though the long-term of complex
systems cannot be predicted, their behavior can be
understood and managed, like a farmer manages the
cultivation of crops.

5. Actuaries can help solve society’s great problems.
Using our unique skills and knowledge – along with the tools
and insights of Complexity Science – actuaries can effectively
address the great problems of complex social systems, and
lead the development of new social policy, rather than merely
administer existing problematic systems.

In exploring these themes, I will use many examples and issues
from health care, because that is where my primary interest lies,
and because the Society of Actuaries (SOA) Health Section funded
this report. But I will also include examples from other actuarial
areas, including pensions, investment, property-casualty, and
reinsurance. The basic concepts, insights, and tools of Complexity
Science apply to all complex systems and all actuaries.

INTRODUCTION 2
Complexity science – an introduction (and invitation) for actuaries
C. ORGANIZATION
The report is organized in three parts and nine chapters:

 Part I – A new science (two chapters) gives an overview
of Complexity Science and agent-based models, and shows
how they relate to the problems of complex social systems.

 Part II – Complexity Science models (five chapters)
introduces Complexity Science models and methods. It
presents four archetypal models of Complexity Science, and
provides the background and tools for you to start applying
them in your work.

 Part III – An invitation (two chapters) presents a vision of
a new type of actuary, the ‘complex systems actuary’, and
proposes a plan to develop this professional.

Each chapter includes exercises to help you better understand its
material. Answers to these exercises are in the document titled
Answers to exercises, found on the SOA web page for this report.
D. SUPPLEMENTAL MATERIAL
Supporting the report is the following supplemental material:

 Top ten Complexity Science books. Among the scores
of books about Complexity Science, ten stand out for
actuaries. They are listed and annotated in the section titled
Top ten Complexity Science books at the end of the report.

 Essential resources. To prepare this report, my first step
was to search for material about Complexity Science that is
relevant for actuaries. In this search, I reviewed thousands of
potentially relevant journal articles, books, web sites,
unpublished reports, and videos. I distilled the results of this
search into about one hundred resources with brief
annotations, found in the section titled Essential resources at the
end of the report. The report’s bibliographic citations (found
in footnotes) refer to these resources.

Because you may want to learn how to perform such a search,
another section at the end of the report, titled Finding the
essential resources, details how I performed the search, and a
document on the SOA web page for this report, titled
Literature search results, details the search results.

INTRODUCTION 3
Complexity science – an introduction (and invitation) for actuaries
D. SUPPLEMENTAL MATERIAL CONTINUED
 Computer code. Until you use it, Complexity Science is
useless. Perhaps the most important material to help you start
using Complexity Science are the models and computer code
supporting the examples in Part II of the report. They are
found on the SOA web page for this report. I carefully
documented the computer code to make it easier for you to
apply Complexity Science models in your work.

To help you set up the computer platforms for the
Complexity Science models, there is a document titled Getting
started with modeling platforms on the SOA web page for this
report.

 Glossary. The report includes a glossary of technical terms.
When a technical term is first introduced, it is bold and in
quotation marks, like ‘new term’.
E. LEARNING OBJECTIVES
After you read this report and work with the Complexity Science
models, you will be able to:
 Explain the basic concepts, tools, insights, and results of
Complexity Science.
 Discuss the most important resources, organizations, and
people in Complexity Science.
 Understand and assess any book, journal article, or other
material about Complexity Science.
 Develop models of complex systems using the modeling
platforms Excel, igraph, and Repast Simphony.
 Explain why Complexity Science is important in actuarial
work.
 Explain how an actuary can become a complex systems
actuary, and why you might want to become one.

I hope you enjoy the report. Even more, I hope you become a
complex systems actuary. If you start along this path, please let
me know. (And please let me know if you have suggestions to
improve this report.)

Alan Mills ([e-mail])
June 10, 2010

INTRODUCTION 4
Complexity science – an introduction (and invitation) for actuaries

PART I: A NEW SCIENCE

I am convinced that the societies that master the new sciences
of complexity and can convert that knowledge into new
products and forms of social organization will become the
cultural, economic, and military superpowers of the next
century.
Heinz Pagels. 19881

1 Pagels (1988), page 53.
Complexity science – an introduction (and invitation) for actuaries
CHAPTER ONE: COMPLEXITY SCIENCE
The movement’s nerve center is a think tank known as the Santa Fe Institute … The researchers who gather
there are an eclectic bunch, ranging from pony-tailed graduate students to Nobel laureates … But they all
share the vision of an underlying unity, a common theoretical framework for complexity that would illuminate
nature and humankind alike. … They believe that their application of these ideas is allowing them to
understand the spontaneous, self-organizing dynamics of the world in a way that no one ever has before – with
the potential for immense impact on the conduct of economics, business, and even politics. … They believe they
are creating, in the words of Santa Fe Institute founder George Cowan, ‘the sciences of the twenty-first century.’
Mitchell Waldrop1
A. INTRODUCTION
How is it that from our cataclysmic origin (the so-called Big Bang)
only about 1017 seconds ago, we now have insurance companies,
pension plans, health systems, and the Society of Actuaries, not to
mention the New York Stock Exchange, the United Nations, and
myriad other social systems? All this in the face of the immutable
Second Law of thermodynamics that says we should instead be
speeding toward a bland soup of hadrons and quarks.

Now that we have such social systems, how will they continue to
develop? Will they smoothly progress toward ever-more
cohesion, efficiency, usefulness, and complexity? Or, like 99
percent of all past life forms, will they soon go extinct?

Why do our social systems take the particular forms they do? Why
do they go through sudden dramatic upheaval, such as the collapse
of the Soviet Union, the 1987 stock market crash, or the recent
financial meltdown? Can we predict the future of our social
systems? Can we manage their evolution? Can we, should we,
optimize their efficiency?

Such questions are the focus of ‘Complexity Science’, a new
field that studies universal principles common to all complex
systems – business firms, countries, galaxies, roses, and children:
how they form, how they evolve, how they die.

Though young, Complexity Science has much to say about such
questions – and much that is relevant to actuarial work. This
chapter presents an overview of Complexity Science, including its
development, hallmarks, concepts, tools, and key results. The
chapter ends with a review of current issues in Complexity
Science and exercises to sharpen your understanding of this new
field.

1 Waldrop (1992), pages 12-13. This book is one of this report’s Top ten Complexity Science books.
ONE: COMPLEXITY SCIENCE 6