SNF Mathematics

Abstract

Our focus will be on the digitization and transformation of the finance industry. In recent years, Fintech companies, defined as organizations that combine innovative business models and technology to enable, enhance and disrupt financial services, have gained substantial funding and are the main drivers of innovation and digitalisation. Projections show that Fintech companies are expected to take away up to 60% of the revenues of the traditional banking sector within the next ten years.

This topic is particularly relevant for Switzerland as one of the main global financial centers. Worldwide Venture Capital (VC) investment in Fintech ventures tripled in 2014 to more than $12 billion, while the Swiss banking industry is substantially lacking behind compared to other world financial centres. As a reaction, the Swiss government has now set Fintech as a top priority on their agenda. This research project will help in the transformation of the Swiss finance industry by laying the academic and mathematical foundations for the use of Fintech in the area of algorithmic strategies, risk management and investment banking. Its academic concepts and conclusions can also be used in a more general context and applied to a larger range of industries.

In particular, the methods developed can also be applied in the context of Industry 4.0. This research is directly related to the goals and deliverables of the COST Action TD1409 (Mathematics for Industry Network - MI-NET)

Research Method

Our methods will be based on sound academic principles and on the most important quantitative techniques from mathematical finance as used in applications.

The analytical work is based on all methods available in financial mathematics. This includes the stochastic modelling of risk factors (prices, interest rates, foreign exchanges rates, and additional indices) as well as the computation of analytical metrics. Our focus here is to adapt these methods in a way that they can be executed in an automated way. This also includes what is called “exception handling” in software engineering.

In a more general way, our approach will be both an interdisciplinary one (involving researchers from other disciplines, institutes, universities and abroad) and one which is based on a close collaboration with the industry. An example is the collaboration with data warehouse experts required for a successful automation of financial analysis.

We will identify important research results that can be applied in the industry and make sure that the problems and results are framed in a way that they can be implemented by researchers from companies. Our approach will combine mathematical techniques as well as practical issues and requirements which we learned when working in an industrial setting and which we aim to extend from the co-operations with the participating companies.

We aim to test our research by leveraging the benefits of the COST network. Through training workshops, collaborations and industry connections, we will disseminate our research results and gain additional insight and requirements. Our approach will be to combine both the academic research and the requirements from the industry.

All that will entirely happen within the COST Action and its network.

Furthermore, we plan to publish our results in the leading academic journals and present the findings at international academic conferences.

Contribution

Scientific impact

The scientific novelty is two-fold: the development of new mathematical techniques to solve industrial problems (long- term impact); and the application of mathematical techniques to the solution of new scientific and technological problems (short-term impact). Innovative mathematics will need to be devised to solve the problems that arise, and this will lead to joint publications in learned journals. Study Groups have a strong track record of taking research through to the publication stage, see for example, the recently-founded academic journals. Mathematics-in-Industry Case Studies and the Journal of Mathematics in Industry. Free boundary problems, partial differential equations to be solved for an unknown function over an unknown domain, are an expository example of how industrial problems can stimulate new areas of mathematical research. The area burgeoned in the 1970s after a large number of problems from industry, including electrical painting, groundwater flow, solidification and melting, were found to fall into this category. A Google Scholar search for 'free boundary problems: theory and applications' now gives 1.5 million results, and there is a dedicated interface and free boundaries journal. Inverse Problems, often known as "parameter identification" problems in industry, are another example of an area of mathematics which have been stimulated by industrial applications. The canonical problem is from the oil (or other mining) industry and concerns finding out where the oil/gas/coal is from seismic measurements at the surface. But many other problems turn out to be of inverse type - whenever you are trying to calculate parameters from limited (either in space or time) data you have an inverse problem which probably does not have a unique solution.

Often mathematical models or techniques devised for one application can be applied to another, seemingly unrelated, application or setting. This knowledge is conserved by mathematicians and that is why study groups are often so successful. “Technology transfer, including the transfer of mathematical ideas, is not a one-way street; a technology designed for or by one company often ends up enriching science as a whole.” (2012 SIAM Report on Mathematics in Industry.) An archetypal example occurred in mathematical finance. Mathematical Option Pricing received a huge intellectual boost when it was realised in 1973 that the Black-Scholes equations were almost identical to the equations for solidification of steel (both are free boundary problems for a diffusion equation). This resulted in the exploitation of a vast body of existing literature going back decades, and has led to a number of researchers in partial differential equations and fluid mechanics turning their attention to financial problems.

Societal impact

Universities in this COST Action will act as centres of cooperation. Industry problems often require a range of expertise, not always to be found within a single mathematics department, or even within a single country. The Action will simplify the process of finding the best partners for relevant EU projects, as well as providing mentoring support for researchers new to the process. This will result in increased participation of less research-intensive countries in Europe.

Economic Impact

Mathematics has huge potential for producing large savings for industry. A 2012 report, commissioned by the UK Engineering and Physical Sciences Research Council (EPSRC), estimated the contribution of Mathematical science research to the UK economy in 2010 to be 2.8 million jobs (around 10% of all jobs in the UK) and £208 billion in terms of Gross Value Added (GVA) contribution (around 16 per cent of total UK GVA). This Action will enable many more industrial problems to be solved or brought to the development stage.