Investigate the Dynamics of Wealth Inequality

Inequality is growing globally and few models are capable of representing the interaction fully. This project aims to examine a model which describes this and evaluate it's accuracy. The model in question is Reallocating Geometric Brownian Motion (RGBM), which incorporates a reallocation term into a Geometric Brownian Motion process. Dependent on the sign of the reallocation parameter wealth either represents taxes (capital flows from rich to poor), or rent (capital flows from poor to rich).
The starting point of the project is to investigate the effect of having a large difference between the typical value and the average value. This continues from findings from our group project of the same name where we discovered that under all types of reallocation, changes in the average value was controlled by the few individuals with a large amount of wealth. Therefore the possibility arises where the amount of wealth in the economy is growing but the wealth of almost all individuals in that economy is reducing.
Data on the wealth of individuals over time is not recorded and hence a starting point for the project would be looking at stock market data. The stock prices of companies share many properties with the wealth of individuals. They are multiplicative in nature, are influenced by the same events (in the case of wealth this can be taxes, for stock prices this can be a global event) and due to globalisation the stock prices of companies have also become more unequal in recent years. This final aspect mirrors the findings from Berman et al. 2016 where by fitting a RGBM model to US personal wealth data they found the reallocation term distributes in favour of the rich.
Other directions of the project would be to investigate properties of the model under the subspace of parameters where in the RGBM model the rich get richer and the overall economy is shrinking.
The context of the research - Inequality is growing globally and few models are capable of representing the underlying mechanisms fully. Typically wealth is recorded as an ensemble rather than over time which is an issue as the wealth of many individuals is not representative of an individuals wealth over time.
The aims and objectives of the research - This project aims to examine the implications of the difference between the time and ensemble averages of wealth within a population. This will be achieved through analysing a model based on Geometric Brownian Motion with the incorporation of reallocation of wealth by individuals. The behaviour of this model is dependent on the level (and direction) of reallocation, an aim of the project will be to understand properties of this model for all types of reallocation.
The novelty of the research methodology - The project will use stock market data as a substitute for wealth data over time to measure the types of interaction between stock prices of various companies and analyse how suitable the reallocation model is for this purpose.
The potential impact, applications, and benefits - The impact of this project is to gain understanding into real-world processes where the difference between averages occurs, identify why it occurs and it's implications. The benefits are a better understanding of the potential flaws from metrics designed to summarise the behaviour of real-world random processes. For example how GDP measures the level of development in a country.
How the research relates to the remit - The project fits into a number of EPSRC research areas, including but not limited to: Complexity Science (as we are studying the effect of interactions in the system), Non-linear Systems (by design the model is multiplicative, and therefore non-linear, in nature) and Statistics and Applied Probability (the model is a stochastic process).
Into which research areas does your research fall? - Global uncertainties, Mathematical Sciences
External Partner - London Mathematical Laboratory

In the 2018 Government Office for Science report, 'Computational Modelling: Technological Futures', Greg Clarke, the Secretary of State for Business Energy and Industrial Strategy, wrote "Computational modelling is essential to our future productivity and competitiveness, for businesses of all sizes and across all sectors of the economy". With its focus on computational models, the mathematics that underpin them, and their integration with complex data, the MathSys II CDT will generate diverse impacts beyond academia. This includes impacts on skills, on the economy, on policy and on society.

Impacts on skills.
MathSys II will produce a minimum of 50 PhD graduates to support the growing national demand for advanced mathematical modelling and data analysis skills. The CDT will provide each of them with broad core skills in the MSc, a deep knowledge of their chosen research specialisation in the PhD and a complementary qualification in transferable skills integrated throughout. Graduates will thus acquire the profiles needed to form the next generation of leaders in business, government and academia. They will be supported by an integrated pastoral support framework, including a diverse group of accessible leadership role models. The cohort based environment of the CDT provides a multiplier effect by encouraging cohorts to forge long-lasting professional networks whose value and influence will long outlast the CDT itself. MathSys II will seek to maximise the influence of these networks by providing topical training in Responsible Research and Innovation, by maintaining a robust Equality, Diversity & Inclusion policy, and by integration with Warwick's global network of international partnerships.

Economic impacts.
The research outputs from many MathSys II PhD projects will be of direct economic value to commercial, public sector and charitable external partners. Engagement with CDT partners will facilitate these impacts. This includes co-supervision of PhD and MSc projects, co-creation of Research Study Groups, and a strong commitment to provide placements/internships for CDT students. When commercial innovations or IP are generated, we will work with Warwick Ventures, the commercial arm of the University of Warwick, to commercialise/license IP where appropriate. Economic impact may also come from the creation of new companies by CDT graduates. MathSys II will present entrepreneurship as a viable career option to students. One external partner, Spectra Analytics, was founded by graduates of the preceding Complexity Science CDT, thus providing accessible role models. We will also provide in-house entrepreneurship training via Warwick Ventures and host events by external start-up accelerator Entrepreneur First.

Impacts on policy.
The CDT will influence policy at the national and international level by working with external partners operating in policy. UK examples include Department of Health, Public Health England and DEFRA. International examples include World Health Organisation (WHO) and the European Commission for the Control of Foot-and-mouth Disease (EuFMD). MathSys students will also utilise the recently announced UKRI policy internships scheme.

Impacts on society.
Public engagement will allow CDT students to promote the value of their research to society at large. Aside from social media, suitable local events include DataBeers, Cafe Scientifique, and the Big Bang Fair. MathSys will also promote a socially-oriented ethos of technology for the common good. Concretely, this includes the creation of open-source software, integration of software and data carpentry into our computational and data driven research training and championing open-access to research. We will also contribute to the 'innovation culture and science' strand of Coventry's 2021 City of Culture programme.