It is with great sadness that we announce that Mark H.A. Davis passed away in March 2020. He lost a difficult, nine-month-long battle with cancer, supported by his beloved wife Jessica.
Mark Davis, 1945-2020. Photo courtesy of Imperial College London.
After earning an undergraduate degree in electrical engineering from the University of Cambridge, Mark joined the Department of Electrical Engineering and Computer Sciences at University of California, Berkeley, as a Ph.D. student in 1968. There he earned his Ph.D. in electrical engineering under the supervision of Pravin Varaiya. Mark had a long association with Imperial College London that dated back to 1972, initially as a professor in the Department of Electrical and Electronic Engineering. After a stint as Director and Head of Research and Product Development for Mitsubishi Finance (later renamed Tokyo-Mitsubishi International)—where he oversaw a team that studied pricing models and risk analysis for financial products—he returned to Imperial College in the Department of Mathematics.
Throughout his career, Mark made impactful contributions in many fields, fostered communities of fellow researchers, and inspired others. He was also an amateur violinist and viola player and performed with various orchestras and chamber music groups.
In light of his passing, Imperial College London has created a website on which everybody can post tributes, reminiscences, and personal feelings.
Here we revisit the personal and professional life of Mark through the words and recollections of his colleagues and lifelong friends.
— Agostino Capponi, chair of the SIAM Activity Group on Financial Mathematics and Engineering (SIAG/FME), on behalf of SIAG/FME officers Birgit Rudloff, Stephan Sturm, and Igor Cialenco
Meeting Mark for the First Time
Tyrone E. Duncan: “I initially became acquainted with Mark during the academic year 1969-1970 when I was visiting the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley. I taught a special course on martingales and Mark was my most interested and involved student, which demonstrates his outstanding abilities. We interacted often about his work on control of partially observed stochastic systems; it was always a pleasure to discuss topics in martingales and stochastic analysis with Mark because he was bright and enthusiastic. He finished the thesis work the following year or two and it was published in the SIAM Journal on Control and Optimization (SICON).”
Steve Shreve: “I first met Mark when he was visiting Washington University in St. Louis. He was staying in the Danforth Mansion, which the university was using as a guest house, and he put me at ease by telling me about the shower with 18 shower heads. In his droll British way, he described how the gurgling water burst forth on him from every possible direction. I later got to experience this particular shower myself; fortunately, I had been forewarned.”
Ioannis Karatzas: “I first came across Mark’s work as a graduate student in the mid and late 1970s while I was roaming the Columbia University libraries for information about stochastic analysis and control. We met in person sometime in 1979, at an MIT seminar on filtering—the hot topic of the day—hosted by Sanjoy Mitter. I was then a postdoc at Brown in Providence, RI, and Wendell Fleming had insisted that I join him on the trip to Boston. Here was this tall, lanky British gentleman — in a T-shirt, with the outward appearance of Telegraph Avenue circa 1968. We hit it off very well and became good friends. Mark and I had long discussions and correspondence on problems of martingale theory, filtering, and control. He had just taken over editorship of the journal Stochastics and was working tirelessly to make it a premier venue in stochastic analysis and its applications. I submitted much of my early work there and did a lot of refereeing for Mark, who supported and encouraged me in my first steps.”
Tomasz R. Bielecki: “I first met Mark during the 24th Control and Decision Conference, which took place in Fort Lauderdale, Fla., in December 1985. I do not recall interacting with him, but I think I attended his lecture. I already knew of Mark’s important contributions to the theory of stochastic control with partial observation, so I was quite excited for an opportunity to see him speak. My first interaction with Mark happened during the 2nd SIAM Conference on Linear Algebra, Signals, Systems and Control, held in San Francisco, Calif., in November 1990. I was presenting a talk in the area of stochastic control and Mark was in the audience. After my presentation, he raised his hand to ask a question. My heart began to race, as by that time Mark was already a giant in the stochastic control community and I was not sure whether I would “survive” his question. Mark must have realized that I was quite tense and asked his question in a jovial way — which was quite characteristic of him, as I learned over the years. His question turned out to be very poignant and proved to be very important for me and my co-author in shaping the final version of our paper.”
Mark’s Remarkable Contributions
Ioannis Karatzas: “I still remember my sense of amazement and awe when I read, and began to understand, Mark’s two landmark 1973 papers in SICON. One of them, with Pravin Varaiya on dynamic programming conditions in non-Markovian stochastic control, had an amazing Doob-Meyer decomposition of the value process, which was universal. This result is the granddaddy of what we now call “optional decomposition” theorems. The second paper, on the existence of optimal stochastic controls, was the most general and easiest-to-read paper on the subject for a long time. But there was a lot more: deep, pioneering studies on the fine structure of filtrations, results on stochastic differentiation and fault detection via non-linear filtering, and work on the Poisson disorder problem and predicted-miss control. I would try to get my hands on and absorb anything from this guy. I knew that, more likely than not, there would be gold in his work.
I suspect that Mark considered me a sort of “younger fellow Ph.D. student.” His advisor at Berkeley was Pravin Varaiya, but he had benefited from advice and discussions with Vic Benes, my own advisor. The three of them, along with Wendell Fleming and Ray Rishel, played a huge role in developing the subject’s basic theory in the late 1960s and early 1970s.
I visited Mark and Jessica at their house near Wimbledon in the fall of 1986.Mark invited me to give a talk at Imperial College — the first time in Britain for me. I found out that he had taken to this new, strange field of finance that Steve Shreve, John Lehoczky and I had been toiling on for a few years. They described some amazing results on the problem of transaction costs about which I knew absolutely nothing, and explained that local times made an appearance there. Really incredible stuff at the time!”
Steve Shreve: “Mark was incredibly prolific. Notable among his contributions was his invention of a theory for piecewise deterministic processes and his introduction of optimal investment with transaction costs to the math finance community. He could always be counted on to give an entertaining, informative talk based on some intriguing new idea. When Mark decided to work on problems in mathematical finance, he took the unusual route of moving to industry for four years, becoming Director and Head of Research and Product Development for Tokyo-Mitsubishi International. This stint informed his research when he returned to Imperial College.”
Wendell Fleming: “In the years after the spectacular success of the Kalman-Bucy filter in the early 1960s, major developments occurred in nonlinear filtering theory. Mark was among the leaders in these developments. His 1980 paper with Steve Marcus, entitled "An Introduction to Nonlinear Filtering," is a standard reference. Among Mark's other contributions was the development of "robust" or "pathwise" solutions to the Zakai partial differential equations of nonlinear filtering.
Among Mark's other notable research contributions was his seminal work on optimal stochastic control for problems with incomplete state observations. This work relied on novel martingale methods. He reported on it at an IFIP Working Conference, which took place in Cocoyoc, Mexico, in February 1982, which is where I first met him. During the 1980s, Mark's main contributions included the notable 1984 paper in the Journal of the Royal Statistical Society on piecewise deterministic processes. Starting in the early 1990s, his interests shifted toward financial engineering, where he enjoyed great success.”
A Mentor, Collaborator, and Inspirational Figure
Ioannis Karatzas: “In June 1993, Avner Friedman organized a weeklong math finance workshop at the Institute for Mathematics and its Applications in Minneapolis, Minn. At the beginning of the week, Mark showed me some notes he had put together on a pathwise approach to the problem of optimal stopping. He presented a very appealing idea: How do you describe the “Lagrange multiplier” that makes a prophet—who can see into the future—behave as if he were a common mortal bound by non-anticipativity constraints? Mark understood the discrete-time version of the problem well but needed help with the continuum. As it turned out, I had exactly the right arrows in my quiver. By the end of the week we had broken the back of this problem: our only joint paper.”
Thaleia Zariphopoulou: “Mark was my mentor. He advised me from the beginning of my career and taught me so much. Working with him was inspirational and I am very grateful to have had this chance. I was always impressed by his mathematical intuition, broad scientific knowledge, and how masterfully he built and combined techniques and concepts. Only much later did I realize that all three enabled him to simply and clearly explain things that were profoundly difficult, both conceptually and technically. I will always cherish the scientific and human interactions I had with him over more than three decades, as well as his wisdom, humor, and laughter.”
Xin Guo: “Mark helped me numerous times at various stages of my career. Our collaboration on impulse control led to a decade-long friendship. In addition to facilitating a very productive and pleasant working experience, Mark—always a gentleman—insisted that he take care of the formatting issues for SICON, as I was a new mom and he felt I should not be bothered by such trivialities. As a mentor and a friend, Mark was generous, kind, and inspirational.”
Wendell Fleming: “Mark Davis was a fine human being and an outstanding mathematical scientist. My encounters with him invariably left me not only better informed but also in a more cheerful mood. He was among a group of exceptionally gifted electrical engineering students at Berkeley during the 1960s and 1970s, several of whom became key figures in this field. The stochastic analysis and stochastic control communities have lost a much admired and respected member.”
Pravin Varaiya: “I was lucky to be Mark's thesis adviser. Mark was brilliant. His groundbreaking thesis developed the martingale approach to the study of conditions for the optimal control of stochastic systems given by Ito equations. The approach permitted arbitrary non-anticipative feedback controls and remains the standard way of formulating stochastic control to this day.”
A Dear Friend
Ioannis Karatzas: “Over the years, Eleni and I crossed paths with Mark and Jessica many times at conferences. But neither Mark nor I ever forgot a chance encounter at a bakery shop on Thera, the island where Eleni and I spend our summers. It made us completely change the way we thought about events of measure zero. As it turned out, Mark and Jessica loved the Greek islands and took frequent tours of them. They visited our house on Thera later that day and met Eleni’s parents, and the next day all four of us went for a swim. Jessica and Mark came to Thera again three summers ago for a stochastic analysis event at the local conference center. This beautiful, joyous occasion is my last memory of a great scholar and a dear friend.”
Xin Guo: “In November 2014, Mark, Jessica, and my family had casual dinner at a restaurant near the popular Berkeley “Gourmet Ghetto.” The food was excellent, and the conversation was “lovely'” (to use Mark's words). In fact, we were so engaged in the discussion that we all completely forgot about moving our cars, which were parked in places with regulated time limits. I received a parking ticket, whereas Mark and Jessica had to trace their towed-away rental car in some very obscure part of Oakland, Calif., in the middle of the night. As usual, Mark's signature laughter and British humor helped turn this incident into a cherished memory.”
Tomasz R. Bielecki: “One encounter with Mark took place in my house in Elmhurst, Ill. Mark was visiting the U.S. to give a talk at the University of Chicago, and my wife and I used this opportunity to invite him and Roger Lee for dinner. I was quite excited to host both of them. But the evening began rather unexpectedly, with me helping Mark fix his glasses (they were partly disassembled because a tiny screw had fallen out and could not be found). Fortunately I had a glasses repair kit at home, and after a few whiles Mark’s glasses were back in shape. I could feel his appreciation, which set the tone for a charming evening. This—together with both Mark and Roger being great companions—resulted in all of us sharing fantastic conversation over dinner and drinks.”
A Major Loss
Steve Shreve: “Our community was blessed to have Mark for so many years. I speak for many when I say that I will miss his technical expertise, wisdom, wit, and friendship.”
Xin Guo: “Many people who knew Mark were familiar with his hallmark laughter, which was full of youthful energy — radiant and contagious even after his first painful surgery. It was heartbreaking for me to hear his weak voice over the phone on March 10th, 2020. This was our last conversation, which lasted for about 40 minutes. He mentioned that it was most difficult for him not to be able to write. I held two of his books in my hand and could not hold back my tears. To cheer him up, I had some flowers sent to him. Mark sent me a merry email promising a photo with the flowers. The photo never came; instead came the very sad news.”
Tomasz R. Bielecki: “Mark was a great researcher, a great personality, and a gentleman. His passing is a profound loss for the stochastics, engineering, and mathematical finance communities. But he will be remembered well and fondly for all the good and important things he achieved.”
A Note from Agostino Capponi (Chair of the SIAG/FME)
Being relatively junior, I only met Mark in person in 2012, when he was a speaker at Ioannis Karatzas' birthday conference. I of course already knew about Mark, especially his contributions to filtering and control — a topic that I had explored during my own Ph.D. thesis. At Joe's Cafeteria on Columbia University’s campus, Mark approached me and asked what I was working on. I was surprised and somewhat intimidated by talking to such a prominent figure, and I did not know what to say. Mark was able to put me at ease. We then had a half-hour discussion on filtering and risk-sensitive control. His guidance and advice on this topic proved very useful for my later work in the context of credit portfolios.
Upon the invitation of Damiano Brigo, I had the opportunity to present my SICON paper on partially observed control for credit portfolios at the Finance and Stochastics Seminars organized by the Imperial College Mathematical Finance Group in 2014. I was intimidated—and at the same time amazed—to see Mark at my seminar. He asked several deep and thought-provoking questions during my talk, and we had an extensive discussion after my presentation. It was clear from his questions and our discussion that he understood the technical complexity and subtleties better than I did. His comments and feedback proved very important for my future research in this area.
We thank the following friends and colleagues of Mark for sharing their memories:
- Agostino Capponi, associate professor of industrial engineering and operations research at Columbia University
- Tyrone E. Duncan, professor of mathematics at the University of Kansas
- Steve Shreve, Orion Hoch Professor of Mathematical Sciences and university professor at Carnegie Mellon University
- Ioannis Karatzas, Eugene Higgins Professor of Applied Probability at Columbia University
- Tomasz R. Bielecki, professor of applied mathematics at the Illinois Institute of Technology
- Wendell Fleming, professor emeritus of applied mathematics at Brown University
- Xin Guo, professor and Coleman Fung Chair Professor in Financial Modeling at the University of California, Berkeley
- Thaleia Zariphopoulou, Presidential Chair in Mathematics and V.F. Neuhaus Centennial Professor at the University of Texas at Austin
- Pravin Varaiya, Nortel Networks Distinguished Professor in the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley