Extreme events and the cumulative distribution of net gains in gambling and structured products Frédéric VRINS† Mikael PETITJEAN* May 25, 2018 Abstract We argue that ethical principles in advertising and market communication cannot be properly discovered and applied to gambling without a deep understanding of its probabilistic implications, in particular when extreme events are influential. We carry out a probabilistic analysis of lottery games with lifetime prizes in order to derive sound recommendations about the pertinent information that should be communicated to nudge gamblers. We propose to focus on the cumulative distribution of net gains, for which there is currently no information available to gamblers. This holds true for structured products in which extreme events matter as well. Keywords: Extreme events, ethical communication, distribution of gains, simulations, gambling, lotteries, structured products. * IESEG School of Management (LEM, UMR CNRS 9221) and Louvain School of Management (LFIN Pole of IMMAQ, UCLouvain). Email:
[email protected]. † Louvain School of Management and LFIN Pole of IMMAQ (UCLouvain). Email:
[email protected] We are grateful to an anonymous reviewer and to several conference participants for their useful suggestions. We also thank Thomas Litwak et David Van der Smissen for their research assistance. We are entirely liable for any mistakes that this document may still contain. 1. Introduction “The ethical principles underlying gambling and their application to activities of which gambling forms a part deserve careful consideration.” This was written by Freeman (1907, p. 76) in the early 20th century in one of the first papers published on gambling in an ethics journal. Although nothing is less true today, we argue in this paper that ethical principles cannot be properly discovered and applied to gambling without a much deeper understanding of its probabilistic implications, in particular in repeated trials.