Joint effects of the liability network and portfolio overlapping on systemic financial risk: contagion and rescue

We examine the conjoined contagion mechanism of the inter-liability network and portfolio overlapping in shaping systemic financial risk. We first develop an iterative algorithm to compute the largest clearing payment vector and price vector, and prove its existence and continuity. A concrete form of total wealth loss is then derived to specify the joint effects of the inter-liability network and portfolio overlapping. Next, we show how inter-institutional liability connections and portfolio diversification can amplify the impact of initial negative shocks and lead later to financial crisis. We prove that illiquidity is a critical factor in triggering risk contagion and that higher inter-institutional leverage can cause larger losses for both the institutions and the outside obligees. Based on the theoretical findings, we propose a rescue strategy via solving a series of linear programs and conclude with some practical suggestions for the management of systemic financial risk.