Mathematics in Financial Markets

The Fundamental Theorem of Asset Pricing

Marta Faias (DM/FCT NOVA)

Marta Faias, PhD holds a BA in Mathematics by the Universidade de Lisboa and a PhD in Economics by the Nova School of Business and Economics, Portugal. She is an Assistant Professor at the Mathematical Department at the FCT NOVA, in doctoral, master and undergraduate degrees. Professor Faias is member of Mathematics and Application Research Center (Portugal) and her research focuses on theoretical issues applied to different topics in Finance (endogenous assets, incomplete markets, indeterminacy, exchange markets formation) and Economics (market games, differential and asymmetric information, public goods provision, club formation).

Abstract: The Fundamental Theorem of Asset Pricing states necessary and sufficient conditions for a financial market to be free of arbitrage (or in other words, for a financial market to not allow for free lunches). This theorem applies not only to simple economies with a finite set of periods and a finite set of states of nature, but also to more general economies with a continuum of periods and continuum uncertainty. In this course, we state and prove the theorem for a simplified economy, and highlight its application.

Cross-Sectional Modeling of Bank Deposits

Sofia Costa (FCT NOVA Alumni, CGD)

Sofia Costa is a Data Analyst in the department of Advanced Analytics of CGD (Caixa Geral de Depósitos). She has an MSc degree in Financial Mathematics (2019) from the Nova University of Lisbon (FCT NOVA) and a degree in Mathematics Applied to Economics and Management (2017) from the University of Lisbon (ISEG).

Abstract: The dynamics of liquidity risk is an important issue in what concerns banks’ activity. It can be approached by studying the evolution of banks’ clients deposits in order to mitigate the probability of bankruptcy and to efficiently manage banks’ resources. In this research, we developed a model that can help banks to properly manage their activity, by explaining the evolution of clients deposits throughout time and simulating possible scenarios with panel data.

Costumer Lifetime Value in Banking Retail

Mariana Mourão (MSc Student MAEBD/FCT NOVA)

Mariana Mourão studied Biomedical Engineering at University of Trás-os-Montes and Alto Douro. MM is a student in the 2nd year of the Master in Analysis and Engineering of Big Data, FCT NOVA. Co-founder of Data Science-FCT Core. In 2018, was a member of the National Association of Biomedical Engineering Students and also a member of the junior company UTAD Solutions Consulting. Currently developing in Millennium BCP data science techniques to find and retain clients that are most valuable to bank. .

Abstract: Companies from several sectors, including banking retail works, aiming to acquire and retain the most profitable customers, try to detect signs, intentions and direct or indirect customer purchase needs. With this purpose, Kotler (1974) introduced for first time the term Customer Lifetime Value (CLV) and defined it as the expected future profit with a given customer based on past and present value. This metric allows to evaluate the impact of different marketing campaigns and to identify the type of campaign that works better, within each segment of customers. In retail banking there are some particular features that must be considered. Those include dealing with discrete transactions, that occur only one time or few times during customer lifetime. Retail banks are however the organizations mostly capable to apply this method as in this sector data regarding demography, consumption patterns income and attitudes towards investment and saving products are typically available.