دانلود کتاب روش‌های امضا در امور مالی، مقدمه‌ای بر کاربردهای محاسباتی

This volume brings together recent contributions on the signature. By happy coincidence it appears at the same time as events marking the 70th birthday of Terry Lyons. Terry was born on 4 May 1953 in London and his formal mathematical career now spans nearly a half century. During this time, he has been a towering influence in British mathematical life and one of the central figures in the development of modern stochastic analysis. He belongs to a generation of mathematicians who helped lay the foundations of the subject, bringing it from a comparatively fringe branch of mathematics to the mainstream area that it is today. Terry’s university education started at Trinity College Cambridge. He graduated with a First in the Mathematical Tripos in 1975. Following Part III at Cambridge he moved to Oxford, completing a DPhil under the supervision of Richard Haydon in 1980. A Junior Research Fellowship at Jesus College, Oxford (1979–81) was followed by a year in the United States as a Fulbright Visiting Researcher and a Visiting Professorship at UCLA (1981–82). From the beginning his work was distinguished by its insight and creativity. His 1980 paper in the Journal of Functional Analysis resolved an open question of Feglede on finely holomorphic functions. A 1983 paper in the Annals of Probability described a simple criterion for transience of a reversible Markov chain. His year in the United States coincided with the first year of his appointment to a Lectureship at Imperial College London (1981–85), the beginning of an association with Imperial that was to be repeated later in his career. Terry’s early research achievements captured the imagination of the community. For instance, his Journal of Differential Geometry paper, “Instability of the Liouville Property for Quasi- Isometric Riemannian Manifolds and Reversible Markov Chains”, showed how probability can be used to solve problems in geometric potential theory. The prizes quickly began to stack up; the Rollo Davidson Prize in 1985 was followed by the Junior Whitehead Prize a year later. In 1985, at the age of 32, Terry was appointed to the Colin Maclaurin Professorship at the University of Edinburgh, where he remained until 1993. During his time at Edinburgh, Terry’s other qualities became more widely evident. He showed an aptitude for academic leadership, becoming Head of Department in 1988, at the relatively early age of 35. He also showed an ability to mentor emerging research talent. Dan Crisan, Alison Etheridge, Ben Hambly, and Michael Roeckner—now prominent figures in their own right—all passed through Edinburgh during Terry’s time there. It was also during this phase of his career that Terry started to lay the foundations for a major new area of research, one which would later become known as the theory of rough paths. Following a return to Imperial College in 1993, the momentum behind the development of rough path theory accelerated. The publication in 1998 of Terry’s article “Differential Equations Driven by Rough Signals” was to become a significant landmark in the adoption of these ideas by stochastic analysts. In 2000 Terry was awarded the Polya prize by the London Mathematical Society. The same year, he left Imperial to become the Wallis Professor of Mathematics at Oxford, succeeding Simon Donaldson. He was elected a Fellow of the Royal Society in 2002, a year which also marked the publication of his book System Control and Rough Paths, co-authored with Zhongmin Qian. This book, together with the notes of Terry’s 2004 course at Saint Flour, attracted an emerging generation of mathematicians to the subject. The 2010s saw rough analysis _lowering into a broad subject. Martin Hairer’s theory of regularity structures built on the principles of rough path theory to understand singular stochastic partial differential equations. While at Oxford, Terry served the wider mathematical community in a number of senior roles. He was Vice-President (2002–03), and later President (2013–15), of the London Mathematical Society, the latter coinciding with the society’s 150th anniversary year. He was Director of the Wales Institute of Mathematical and Computational Sciences from 2007 to 2011. He also played a key role in the establishment of the Oxford-Man Institute, an interdisciplinary institute, serving on its Executive Committee for eight years, including a period as the Institute’s Director from 2011 until 2015. He has been recognized by learned societies across the United Kingdom and is both a Fellow of the Learned Society of Wales and a Fellow of the Royal Society of Edinburgh. He has been decorated with honorary degrees by the Universities of Paul Sabatier Toulouse and Waterloo and has been awarded Honorary Fellowships by the University of Aberystwyth and Cardiff University. A significant recent contribution in Terry’s career has been the development of rough path-based methods in data science. Central to this has been the Chen-Fliess series or “signature”. The breakthrough 2010 paper of Terry and Ben Hambly in the Annals of Mathematics provided the theoretical foundations. The combination of these abstract tools with recent advances in data science, has led to development of a powerful set of Machine Learning tools for “streamed” data. Much of the progress has been pioneered by the Data Sig project, a prestigious six-year EPSRC Programme Grant, which Terry has managed as Principal Investigator since 2019. Terry has been, and continues to be, a role-model, mentor, and a source of inspiration to successive generations mathematicians. It seems fitting that this volume should focus on the theory and applications of the signature. Its subject matter provides one recent example in which Terry’s ideas and creativity have been instrumental to initiating a whole new area of mathematics.