Chaos, Solitons and Fractals 29 (2006) 517–519

www.elsevier.com/locate/chaos

My chaotic career—from billiard balls toeconomic dynamics and financial markets

I would first of all like to thank Laura Gardini, Gian Italo Bischi and Iryna Sushko for organizing the MDEF 04Conference and the associated special issue of Chaos, Solitons and Fractals and in particular for dedicating these to my60th birthday. Special thanks are due to Shahriar Yousefi for so carefully overseeing the editorial process involved inthe production of this special issue. I would also like to express my gratitude to all participants and particularly thosewho I know made a special effort to attend what is always an excellent conference in Urbino.

My visit to Urbino for the occasion of MDEF 04 marked my seventh annual pilgrimage to this beautiful, remarkableand remarkably well preserved Italian hill town whose roots go back to the highpoint of the Renaissance. For a math-ematical economist with a strong research interest in modelling key economic adjustment processes as non-lineardynamical systems it is not only the beautiful buildings, churches and palaces reminding us of a glorious past thatare the attraction of such regular visits. This is also a place where some of the world�s most advanced work on the the-ory of non-linear dynamical systems is being carried out. Laura and Gian Italo have created around them a group ofbrilliant researchers in this area whose network and influence now extend to all corners of the globe. I regard the oppor-tunity to collaborate with this group as one of the high points of my career.

I suppose when one reaches one�s 60th year one is entitled to reflect a little on one�s path through life. During thisvisit to Urbino I had occasion to reflect on how far my career has taken me, both in the geographical and the intellectualsense. In my final high school years in Sydney I found that I had an aptitude for mathematics and physics and I realisedthen that I wanted to do something in life that would involve the use of mathematics. At that time the idea that the‘‘something’’ would involve economics and finance was totally absent from my mind. In my generation those giftedin mathematics and physics thought about careers in science or engineering. So in 1961 I entered the University of Syd-ney with the intention of studying electrical engineering, however after six months I realized that I was not cut-out to bean engineer and so I switched to the Science Faculty to major in applied mathematics.

At the University of Sydney in that era one studied what would now be known as classical applied mathematics. Inthe first year we studied classical mechanics, which in fact proved to be an excellent training in the basic principles ofmathematical modelling. My most enduring memory of that year was the set of (quite difficult) problems involving themotion of colliding billiard balls. In later years we studied the tools and analysis needed to solve all manner of ordinarydifferential, partial differential and integral equations with applications to a wide range of areas such as electromagnetictheory, fluid mechanics, seismology, acoustics and nuclear reactor theory. I went on to complete a Master of Sciencedegree in applied mathematics, for a thesis that considered various ways of computing the complex error function. Formy Ph.D. work I switched to the University of New South Wales (also located in Sydney) and wrote a thesis on nuclearreactor theory. This essentially involved solving the integral equations governing the slowing down of neutrons throughvarious geometric configurations of U235 and heavy water. During my Ph.D. candidature I held a Fellowship that alsoallowed me to gain some teaching experience at the university�s Wollongong campus (80 km to the south of Sydney).Looking back I realized that the research training and teaching experience from that period have stood me in goodstead throughout my academic career.

This was also a period in my life when I became interested in studying languages, as I had decided I wanted to spendsome time in Europe after completing my Ph.D. As was common for my generation I had studied French right throughHigh School but could not speak a word, so I took conversation classes that eventually got my French to a respectablelevel. I also studied Italian, the language of my parents and that I feel I am still learning, though I must say the manyvisits to Urbino have been very influential here as well. Later in life I started studying Chinese, an enterprise in which

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518 Personal report / Chaos, Solitons and Fractals 29 (2006) 517–519

I am still engaged. The interest in Chinese language and culture was inspired by the fact that my wife of thirty years,Lyn, is Malaysian-Chinese.

After completing my applied mathematics Ph.D. in 1969 I was awarded a French Government Technical Scholar-ship that enabled me to spend two years at the University of Nancy where I did research on optimisation methods at thecomputing centre. During this period I was able to perfect my French and also travel around Europe. I was particularlyglad to be able to travel to Italy and visit the Calabrian towns from which my grandfathers had emigrated. Though for awhile I wondered if the effort to learn Italian had been worth-while. I felt very proud with how I had managed with thelanguage on the streets of Florence and Rome, but when I got to Calabria I felt totally at a loss as I found the localdialect and accent almost incomprehensible, though at least my relatives understood my Italian, so some communica-tion was possible.

On returning to Australia in 1971 I took up a lecturing position in the School of Mathematical Sciences at the NewSouth Wales Institute of Technology (which later became the University of Technology, Sydney). Apart from a threeyear spell at the University of New South Wales from 1986–1989, this is the institution at which I have spent my entiresubsequent career. The teaching load in those years was heavy, but I managed to find time to do something about mylong held interest in economics and enrolled in the Master of Commerce program at the University of New SouthWales, which I completed in 1975. I then went on to do a Ph.D. in Economics at the same university.

During this period three influences were decisive for my later career. One of my lecturers, Warren Hughes (muchlater a Dean at the University of Waikato in New Zealand) introduced me to option pricing as he asked for my helpin trying to read Merton�s classical paper on option pricing under jump-diffusions. We subsequently wrote a paperapplying the model to Australian data. It was as a result of this grounding that much later in my career I returnedto option pricing and this has become one of my main research interests. The second decisive influence was MurrayKemp, who was a Research Professor in the Faculty of Commerce at the University of New South Wales. I had takensome courses in mathematical economics from him and had found them very interesting. Murray got me interested inseveral problems involving deterministic optimal control applied to economics and a number of papers evolved out ofthis work. Murray suggested that I write this work up as a Ph.D. in economics, as this would help me to obtain a teach-ing position in economics, which by this time I felt would better match my research career interests. On the path to thePh.D. I spent a study leave period in 1982 at the University of Louvain which proved to be the third decisive influence.Whilst I was there I attended a workshop on the, then �new�, macroeconomics. One aspect of the new macroeconomicsthat seemed to be accepted without question by most of the profession, but with which I had great difficulty, was the useof the so-called jump-variable technique. This is a procedure whereby stability is imposed on models whose dynamicsare usually characterized by saddle point instability. What is also intertwined with this procedure is the notion ofrational expectations, which was taking such a strong grip on the profession at that time. I had always had (and stillhave) the greatest difficulty accepting this notion as a useful one for helping us to understand how the real economyworks. It seemed to me that what was being overlooked in much of this analysis is the fact that the instability encoun-tered in these models is only local instability. If one were to adopt a global and nonlinear viewpoint a far richer set ofoutcomes would be possible in which stability need not be imposed but would rather result from the global evolution ofthe economic dynamics. On returning to Australia I told Murray that I wanted to change entirely my thesis topic andwrite a thesis on the nonlinear viewpoint in economics. He was surprised, especially since a thesis on the original topicwas almost completed, but he did allow me to submit a thesis on the alternative topic. The thesis was eventually pub-lished in the Springer-Verlag Lecture Note Series, in fact through the good offices of Hans-Walter Lorenz with whom Ihad come into contact through our mutual interest in nonlinear economic dynamics and who recommended the thesisfor publication. By now an important part of my research career had been set. It was my desire to model the global andnonlinear aspects of economic adjustment processes and dissatisfaction with the rational expectations paradigm thatdeveloped into what has become a large research agenda in nonlinear macroeconomic dynamics and heterogeneousagent modelling.

In 1986 I was appointed to a teaching position in the School of Banking and Finance at the University of New SouthWales. This allowed me to rekindle my research interest in option pricing, though at the same time I pursued my workon nonlinear economic dynamics. Whilst I was only three years in this position it proved to be quite an influentialperiod of my career, I had much more time for research than I had had at my former institution where the focushad been mostly on teaching. In 1989 I was appointed as a Professor in the School of Finance and Economics atthe University of Technology, Sydney. Whilst the basic foundations of my research agenda in economic dynamicsand option pricing had been established over the previous decade, it was at UTS that this agenda came to fruition. Thiswas because, for various reasons, the School of Finance and Economics offered me several opportunities I had lackedearlier in my career. The first was the opportunity to travel to international conferences. I was grateful for this oppor-tunity as it enabled me to attend the Vienna Workshops on Economic Dynamics initiated by Gustav Feichtinger, thefirst of which I attended in 1991. These meetings were (and continue to be) a great source of intellectual inspiration for

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me and it was in Vienna that I first made personal contact with several people who have proved to be quite influential inmy career, for instance Peter Flaschel, Willi Semmler, Hans-Walter Lorenz and Cars Hommes. I also renewed contactwith Volker Bohm whom I had met whilst he was visiting the University of New South Wales in 1987. It was whilstattending another conference in Dublin in 1991 at a session on oligopoly dynamics organized by Koji Okuguchi thatI first met Ferenc Szidarovszky, another link that has proved to be important in my career. Subsequently I have beenable to travel to many conferences and Universities around the world, but I should in particular mention the Universityof Urbino and the University of Bielefeld which in a sense have become second homes for me. The second opportunityoffered to me by the School was to invite some of my international research collaborators to make short visits to Syd-ney. I cannot list all those who have come over the years but I should mention the almost annual visits by Peter Flascheland the quite frequent visits by Volker Bohm and Ferenc Szidarovszky. The third opportunity was funding support fora number of brilliant individuals who chose to carry out their PhD studies under my supervision. Again I can�t mentionthem all here, but I should single out Tony Xue-Zhong He who has gone on to be one of my important collaborators inthe research agenda into heterogeneous agent models.

The link with Urbino, which is now so important, in fact developed slowly. Sometime during the late 1980s I joinedAMASES (Associazione per la Matematica Applicata alle Scienze Economiche e Sociali), mainly because I wanted tosubscribe to their journal—Rivista di Matematica per le Scienze Economiche e Sociali—which had published one of myjoint papers with Koji Okuguchi. As a result I received their annual conference proceedings and it was through thesethat I first became aware that a number of Italians were working on models of non-linear economic dynamics. I notedin particular some of the early papers in this area by Laura Gardini. In 1998 I was finally able to visit Urbino for thefirst time and make personal contact with Laura, Gian Italo, Roberto Dieci and Anna Agliari just to mention the mostprominent in the Urbino group. The now annual visits to Urbino have become an important part of my annual scheduleand are rich not only in intellectual achievement but also in personal interactions.

Before concluding I should make two acknowledgements. The first is to the University of Technology, Sydney whichin so many ways has provided sustained support for my research agenda over fifteen years. The second is to my wife,Lyn. Without her support for my commitment to a busy academic career throughout our entire married life none ofwhat I have achieved could have been achieved.

Carl ChiarellaThe School of Finance and Economics

University of Technology

Sydney

Tel.: +61 2 9514 7777; fax: +61 2 9514 7722

E-mail address: carl.chiarella@uts.edu.au