Collective Risk Measures for Processes

Abstract This paper develops a comprehensive framework for collective risk measures, tools designed to quantify the aggregate risk stemming from a collective of agents. Crucially, these measures explicitly account for inter-agent cooperation, allowing agents to exchange risk through state-dependent transfers without requiring external capital flows. We review previous works on no-arbitrage in the collective framework, and introduce collective risk measures for both random variables and stochastic processes in discrete time. In the latter case, we allow for time-dependent cooperation and risk sharing, supporting a consistent evaluation of evolving financial positions within a collective framework. Among the several applications of the theory, we study collective super-replication prices and we provide dual characterizations of collective risk measures via families of (martingale) measures.