This article introduces the concept of duality in financial networks, which entails the division of losses versus gains. In bankruptcy problems, in which a bankrupt entity divides its non-negative assets among a group of claimants, duality is well understood. Financial networks generalize bankruptcy problems by allowing for multiple agents with individual assets interconnected by mutual claims. We argue that allowing for negative assets is imperative to adequately formulate duality for financial networks. We show that there is a linear relationship between transfer schemes based on claims rules in a financial network and transfer schemes based on the dual of those claims rules in the dual financial network. Moreover, dual financial networks enable us to define dual transfer rules and dual allocation rules. We show that both self-dual transfer rules and self-dual allocation rules have to be based on self-dual claims rules. On the other hand, we demonstrate that transfer rules based on self-dual claims rules need not be self-dual, whereas allocation rules based on self-dual claims rules are always self-dual.
We analyze risk-taking behaviors of financial institutions linked through cross-shareholding relationships. We endogenize risk exposure accounting for default risk by modeling Value-at-Risk-based risk-management – that is targeted default probabilities – in the presence of extreme risk on asset return. We relate risk-taking behaviors to a centrality measure that captures the propagation of losses within the network, and show that network integration increases risk-taking levels and expected return. However, we show that network integration also results in larger expected shortfall, indicating greater exposure to losses for creditors. We explore the impact of the cross-shareholding network on the implementation of regulation, particularly through capital requirements, and identify key institutions, those with the highest influence on aggregate investments in risky assets.
In this paper, we explore the issue of manipulability in the setting of financial systems by considering two weak forms of immunity: merging-proofness and splitting-proofness. Not surprisingly, splitting-proofness conflicts with basic requirements such as the priority of debt over equity and the limited liability of equity. Remarkably, we provide a comprehensive characterization of the class of bankruptcy rules that gives rise to financial rules that satisfy merging-proofness.