Professor Richard Vinter and Professor Harry Zheng pay tribute to the late Professor Mark Davis of the Department of Mathematics.

Professor Mark Davis died in March 2020, aged 74. He had been ill since June 2019, suffering from cancer.

Mark had a long association with Imperial College dating back to 1972, initially in the Department of Electrical and Electronic Engineering, where he became professor and, after a period working as a research director in the finance industry, in the Department of Mathematics.

He was an internationally recognised figure in stochastic analysis, stochastic control and financial mathematics who, through his innovative ideas and expository skills, was an inspiration to several generations of researchers and practitioners in these fields.

Mark graduated in Electrical Engineering at the University of Cambridge and then obtained his PhD degree at UC Berkeley under the supervision of Pravin Varaiya. Mark early displayed his talents as a researcher. His PhD research initiated the martingale theory of stochastic control. Its significance was immediately recognised and remains, to this day, one of the main methodological approaches in stochastic control and optimisation.

This was to be just the first of a number of important advances he was to achieve over his career, including the formulation and systematic investigation of the class of piecewise deterministic processes, leading to his influential research monograph in this area.

Returning from the USA, Mark joined the Control Group at Imperial College London.  Research visits to Harvard, the Banach Center in Warsaw, Stanford, University of Minnesota, University of Oslo, MIT and the University of Vienna were important to Mark's development over the next three decades and the basis of fruitful research collaborations.

By the early 1990's Mark had developed a strong interest in applications of stochastic analysis to mathematical finance and had achieved wide recognition in the academic community for his work in this area. Feeling the need for more hands-on experience, in 1995 he accepted the position of Director and Head of Research and Product Development for Mitsubishi Finance (later renamed Tokyo-Mitsubishi International), where he ran a team working on pricing models and risk analysis for financial products.

Mark returned to Imperial College in 2000 to create Imperial's Mathematical Finance group. He launched the College's highly successful MSc in Mathematical Finance, designed by Terry Lyons, and served as director for many years while continuing vigorously to pursue his research interests.

Mark was Editor-in-Chief of Stochastics and Stochastics Reports for 17 years, during which period he built up the journal into one maintaining the highest standards, and created a network of fellow researchers, working in a spirit of cooperation, encouragement and friendship. He authored six books on stochastic analysis and published over 100 journal articles. His last publication, 'Mathematical Finance: A Very Short Introduction', demonstrates, beyond his academic achievements, his exceptional gifts for communicating complicated ideas to a general audience.

Throughout his academic working life Mark was ably supported by his secretary Doris Abeysekera whose hard work and energy also greatly aided his publishing activities. For this and the frequent help and encouragement she gave to his research and graduate students he was enormously grateful.

Outside his academic work Mark had many interests. Along with his wife Jessica, he was an amateur violinist and viola player and enjoyed many hours playing in orchestras and chamber music groups. Other activities included hiking, swimming and cycling and the joy of foreign travel, frequently attached to conferences. He enjoyed socialising with a wide circle of friends from many different backgrounds, going to concerts, theatre and films, in all of which Jessica was his ever present and enlivening companion.

The Society for Industrial and Applied Mathematics' (SIAM) tribute to Mark, with further words and recollections from colleagues and lifelong friends.

The journal Stochastics: An International Journal of Probability and Stochastic Processes (as the former Stochastics and Stochastics Reports is named), plans to publish a special issue dedicated to Mark and to organise a special workshop in commemoration.

Friends and colleagues of Mark are invited to share their own tributes and memories through the comments section below.