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Foreword to the Special Issue Devoted to Professor Ivar Ekeland's 70Th Math Finan Econ (2014) 8:321–325 DOI 10.1007/s11579-014-0130-4 Foreword to the special issue devoted to Professor Ivar Ekeland’s 70th birthday Elyès Jouini Received: 12 September 2014 / Accepted: 17 September 2014 / Published online: 25 September 2014 © Springer-Verlag Berlin Heidelberg 2014 It is a great pleasure to write this foreword and to dedicate this volume to our colleague, friend and mentor Ivar Ekeland. Ivar became 70 years old on July 2, 2014 and more than 80 colleagues and friends convened to celebrate his anniversary at the conference organized from June 18 to June 20 at the Université Paris-Dauphine. Fifteen invited talks were pre- sented covering his broad research fields: from nonlinear functional analysis, calculus of variations, optimal transport and Hamiltonian dynamics to mathematical economics, math- ematical finance and philosophy of sciences. In all these fields, Ivar has been a leader and an innovator for the past 40 years and there is no sign of slowing down at the time of his 70th birthday. In particular, Ivar Ekeland is a very active member of the Finance and Sustainable Development Chair as well as of the Finance for Energy Market Research Centre at the Université Paris-Dauphine. It is hard to describe the whole career of Ivar and even harder to describe all his contribu- tions. Therefore, I will just mention the main milestones of his career and mainly focus on the contributions that are at the interplay beween mathematics, economics and finance. 1 Ivar’s career milestones Ivar Ekeland was born in 1944 as son of a Norwegian diplomat and a French mother. He obtained his baccalaureat at the Lycée Français de Vienne after what he prepared the compet- itive examinations of the French Grandes Ecoles at the Ecole Sainte-Geneviève, Versailles. His scientific career began at the École normale supérieure in Paris. At age 26 he was already a professor at the Université Paris-Dauphine - a year later vice-rector. He was also a founding E. Jouini (B) PSL, Univ. Paris-Dauphine, CEREMADE, Paris, France e-mail: [email protected] E. Jouini CNRS, UMR7534, Paris, France 123 322 Math Finan Econ (2014) 8:321–325 member of the research group CEREMADE - one of the most successful research platforms with mathematical emphasis - and he is still an active member of this research group. From 1989 to 1994 Ivar Ekeland was president of the Université Paris-Dauphine, from 2003 to 2008 he headed the Pacific Institute of Mathematical Sciences in Vancouver. Between 2003 and 2011 he held also the Canada Research Chair in Mathematical Economics at the University of British Columbia. Ivar is member of the Norwegian Academy of Sciences. 2 Ivar’s main contributions Ivar Ekeland developed an extensive research in pure and applied mathematics. His insight and vision and his appetite for new problems is proven by his continued, deep and varied contributions across mathematics, economics and finance. His scientific oeuvre includes about 100 original papers in the field of pure mathematics and about 50 in the field of their applications. Ivar Ekeland is, in particular, known as the author of Ekeland’s variational principle [4] that opened a new era in the calculus of variations by exploring the concept of nearly optimal solutions. Ekeland is also known for his use of the Shapley–Folkman lemma in optimization theory [8]. He has contributed to the periodic solutions of Hamiltonian systems and partic- ularly to the theory of Kre˘ın indices for linear systems [6]. In economics, his contributions include hedonic pricing that implicitly price out the attributes that characterize goods [12]or the characterization of the aggregate behavior of a group in a market environment through the exploration of the mathematical structure of such aggregation problems [8]. In finance, he contributed, in particular, to the environmental finance field working on ethical interest rates. Besides his talents as mathematician, I would like to underline two remarkable qualities of Ivar Ekeland. The first one is his interest in popularizing mathematics. He has written numerous books in which he has explained parts of dynamical systems, chaos theory, and probability theory. Some of these books are for a very young public [9]. Furthermore, through these writings, Ivar Ekeland helped to inspire the discussion of chaos theory in Michael Crichton’s 1990 novel Jurassic Park [7]. Ivar Ekeland’s popular science books have received numerous awards, both for their mathematical precision and for their educational and literary value. Ivar Ekeland was awarded both the d’Alembert and Jean Rostand Prizes. The second one is his capacity to establish connections between very different fields. This is better summarized by Jean-Michel Lasry who writes about his contribution in the current volume « My aim, in this short paper, is to show how serendipity was a key input in the research that led Ivar to two of his main contributions: proof of an old Hamiltonian systems conjecture using devices from the mathematical economics tool box, then smart investigation of family’s budget decision process using symplectic geometry. Of course anyone is expected to say: “you mean: symplectic tools for Hamiltonians, and mathematical economics toolkit for family budget”. Brave new world. » Ivar has been also the first one, since Kantorovich in the 40’s, to link the theory of optimal mass transport to important problems in mathematical economics. For instance, Ivar noticed long ago the connection between cyclical monotonicity conditions appearing in optimal transport as in [13] and the implementability condition in incentive theory [15]. Ivar deeply influenced a stream of research which gathered mathematicians and economists and raised a variety of new problems. Ivar did so in joint papers on hedonic models with James Heckman [12], and on the structure of cities with—his then student—Guillaume Carlier [2]. 123 Math Finan Econ (2014) 8:321–325 323 This allowed them to extend the work of [14] on equilibria in urban economics beyond the radially symmetric case. These models motivated him to study (and let study) Monge- Kantorovich problems with general cost—as opposed to the well known quadratic cost pop- ularized by [1]—and let him to develop a corresponding theory of c-convexity. Again, moti- vated by economic models, he introduced an important and natural class of cost functions for multidimensional Monge-Kantorovich problems. They are of the form m c(x1, ..., xm) = inf ci (xi , y) y∈Y i=1 where each ci is a 2-marginal cost. These remain essentially the only cost functions for which the multidimensional transport problem has been resolved so far in Euclidean space as well as manifolds. 3 Contributions in honor of Ivar Ekeland Besides his scientific qualities stressed above, I would like to emphasize Ivar’s human qual- ities. Everyone would agree to recognize his exceptional openness, his great kindness, his great listening skills, his sense of duty and his availability to others when needed. I personally experienced the latter just after the Tunisian revolution when I had to join the newly formed government. Ivar agreed to replace me as Editor in Chief of Mathematics and Financial Eco- nomics at very short notice. When he passed this responsibility to Ulrich Horst in 2014, we thought, Delphine Lautier, Ulrich Horst and I that Ivar’s 70th birthday deserved a special issue of this journal because he headed it during 3years but mainly because mathematics, finance and economics are at the very heart of Ivar’s fields of interest. To achieve this aim, we invited distinguished researchers among Ivar’s friends and co- authors. All contributions to this issue are new and original. They have been subject to the regular peer-review process. These papers illustrate Ivar’s fields of interest but also how Ivar influenced these fields as well as the contributors. However, we do not pretend to cover all Ivar’s fields of interest nor all fields to which he contributed. The papers by Blanchet and Carlier and by Ghoussoub and Moameni are directly related to Ivar’s optimal mass transportation contributions mentioned above. Walter Schachermayer contribution is based on duality theory and, as he explains, “A long time ago, deep in the previous century, Karl Sigmund gave me a copy of Ivar’s small booklet on game theory and mathematical economics [5]. There I learned to appreciate the power of duality theory, which finds very natural applications and interpretations in the economic context. The Hahn–Banach theorem—and its offsprings like the minimax or the bipolar theorem—takes a central place in this approach. The systematic use of duality theory then was a guiding principle for much of my scientific work. The present paper presents one more application of the bipolar theorem in an economic context.” Santiago Moreno and Jean-Charles Rochet paper is on applications of the dividend- distribution problem in continuous time to corporate-finance models. The dividend- distribution model is a classic in mathematical finance, but only recently has it been applied to corporate finance. It shows the interest for mathematicians to enlarge the scope of their research and develop true collaborations with other fields. Ivar has been a constant advocate of such collaborations. Furthermore, the paper makes use of optimal-control methodology, 123 324 Math Finan Econ (2014) 8:321–325 a field in which Ivar has been active for many years and one that owes much to him, both in terms of development and dissemination. The contributions of Dutta and Polemarchakis are related to the work of Ivar and Pierre- André Chiappori on aggregation [3], in particular under uncertainty. One of Ivar’s important contributions to Economic Theory is in the field of “hedonic mod- els”, which aim at explaining how the quality of a good determines its price in a supply-and- demand equilibrium framework.
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