This talk explores the field of collective phenomena in financial markets, where cooperation and interaction among agents redefine core concepts. We build upon classical no-arbitrage theory to introduce a multi-agent perspective, revealing novel insights into market efficiency and risk management. A cornerstone is the work by Biagini et al. [1], which established Collective Arbitrage and Collective Super-replication in discrete time, demonstrating how risk-sharing significantly reduces hedging costs. This necessitates the No Collective Arbitrage (NCA) condition as an essential extension of classical no-arbitrage. We further examine the implications for market completeness and replication, presenting Doldi et al.’s formulation of the Second Collective Fundamental Theorem of Asset Pricing [3]. Their work defines No Collective Arbitrage prices for claim vectors and characterizes them via collective martingale measures. Finally, we offer a complementary perspective on collective risk measures in both dynamic [4] and process-based settings [5] and analyze how inter-agent cooperation influences risk assessment over time, focusing on aggregation properties and time consistency.

References

[1] Biagini, F., Doldi, A., Fouque, J-P., Frittelli, M. and Meyer-Brandis T. (2025). Collective Arbitrage and the Value of Cooperation. Forthcoming in Finance and Stochastics.

[2] Frittelli, M. (2025). Collective Free Lunch and the FTAP. Siam Journal of Financial Mathematics, Vol. 16, No. 1, pp. 53–67.

[3] Doldi, A., Frittelli, M. and Maggis, M. (2025). Collective completeness and pricing hedging Duality. Math. Fin. Econ..

[4] Doldi, A., Frittelli, M. and Rosazza Gianin E., (2024). Collective Dynamic Risk Measures. Frontiers of Mathematical Finance, Vol. 3(3), pp 376-399.

[5] Doldi, A., Frittelli, M. and Rosazza Gianin, E. (2025). Collective Risk Measures for processes. submitted.