Insurance risk analysis of financial networks vulnerable to a shock

We conduct a risk analysis of non-core insurance business of selling protection to financial firms against investment losses due to a shock. A static structural model is constructed, composed of a network of firms who cross-hold each other, a financial market consisting of multiple primitive assets that are vulnerable to a shock, and an insurer who resides external to the network and assesses the opportunity to sell protection to the financial firms. Assume that each firm in the network is rational and able to decide how much protection to purchase to optimize its portfolio according to the mean-variance principle. As a result, the shock may impact on the insurer but indirectly through the network. In view of the robust-yet-fragile nature of financial networks that has been discovered, both empirically and theoretically, by various recent works, one expects that the network integration and the shock play an intertwined role in the insurance risk. Our study forms a theoretical confirmation of this surmise: Depending on the shock size, there are three mutually exclusive scenarios in which an increase in the network integration can either reduce or amplify the impact of the shock on the insurance risk.