The public bailouts of financial institutions during the Financial Crisis of 2007-2009 have resulted in the degradation of public trust in the financial system. Less well known is that mathematics has been criticised by the regulators, professional bodies and civil society as having contributed to financial crises by placing a veil over financial practice. This project looks to restore public trust in both finance and mathematics.
The project is specifically concerned with the observation that banking systems with a significant component of not-for-profit institutions required less public support during the Crisis than systems dominated by private banks. This observation will be considered in the context of a theoretical basis in moral philosophy: what is the relationship between ethics and the structure of the polis. In particular, is the observed difference in bailouts a consequence of differing commercial cultures and will a system based on reciprocity perform better than one based on profit maximisation? The motivation for this approach is that legislatures in both the UK and US identified a decline in commercial ethics as being significant causal factor in the Crisis and has emerged out of my experience as the RCUK Academic Fellow in Financial Mathematics between 2006 and 2011.
The project is centred on research that will investigate the resilience and effectiveness of financial systems based on different commercial cultures using techniques from Applied Probability and Complexity Science, in particular Stochastic and Adaptive Networks. The research question of this project is to determine whether financial systems are more or less resilient and effective if based on different commercial cultures, e.g.: profit/loss sharing (Islamic musharakah), if loan interest is based purely on objective risk born by lender (Scholastic usury prohibition), if the interest rate is determined by the opportunity cost (market based) or if interest aims to maximise returns to the lender. It will model financial systems as graphs and study how the different commercial cultures affect the evolution of the graph topology, and then how money/credit is transmitted on different graph topologies. Effectiveness will be measured by the efficiency in enabling lending and resilience by the ability of a financial network to withstand shocks generated by losses. This research question addresses an issue moral philosophy: what is the relationship between ethics and the structure of the polis and is motivated by the thesis that reciprocity emerges as a social norm in communities where exchange is important (e.g. ).
The hypothesis of the project is that there will be greater homophily between the agents in a financial network based on reciprocity than in a network focused on profit maximisation and this will create more resilient and effective financial networks (e.g.  in a different context). The objective of the project is to employ mathematics to test the hypothesis in support of the view that the ethical concept of reciprocity is intrinsic to the development of successful markets. These views are rooted in the Aristotelian position that ethics are the practices that sustain communities, and reciprocity is a virtue internal to market exchange, topics of Pragmatic philosophy and contemporary Virtue ethics.
The project is a response to financial crises and scandals since 2007. In particular, in 2012 I organised the 2013 IMA Conference on Mathematics in Finance with participation from the Bank of England. The representative of the Bank highlighted the need for mathematicians to shift their perspective away from stochastic calculus and re-focus from micro- to macro-economic issues and address the concerns identified in [10, para. 89, v. II], that mathematics aids ‘insincerity’ in financial practice. A key priority for the Bank was in developing network models of the financial system, building on  and . Simultaneously there have been calls from, so-called, heterodox economists for their profession to focus on economics as a complex, evolving system (e.g. , [9, ‘The way forward’], ). Finally, there is a general concern with commercial ethics (e.g. ) along with a scholarly recognition that commerce can have a positive role in morality (e.g. ). Influenced by these external factors the PI has developed the thesis, in , that reciprocity, not profit maximisation, is the foundation of of the Fundamental Theorem of Asset Pricing of Financial Mathematics.
Since the Financial Crisis there has been accelerating interest in applying Network Theory to investigate financial systems. The novelty of this project is it is concerned with different commercial cultures, the structures of financial networks that these cultures generate and their different behaviours. Specifically, it does not assume that the objective of a financial agent is to maximise profit. This immediately connects the project to researchers seeking to re-orientate finance and distinguishes the approach taken in the project from existing approaches that are based on the conventional economic assumption of utility maximisation.
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