In recent years, there has been an increasing interest in the study of systemic risk, which was intensified by the financial crisis. Systemic risk is a property of systems of interconnected components in which the failure of individual components can lead to the failure of others. Such cascades of failures can occur in various types of system, including power grids, computer networks, financial or interbank systems, and also human populations in the case of epidemics. Most of the current literature in this field is descriptive, and the role of strategic interactions is much less emphasized. The goal of this paper is to study how the strategic solicitation and provision of insurance can affect systemic risk.
The theoretical tools used to study this problem lie at the intersection of statistical physics and game theory. Agents are assumed to be connected through a network, and each can choose to insure or not against the failure of a neighbor. A Bayes-Nash equilibrium, in which agents form a mean-field expectation of a neighbor's effective failure probability, is derived. In a subsequent stage, each agent can also act as a provider of insurance, resulting in the creation of an insurance network. A co-epidemic model is then used to study the interaction of cascading failures on the contagion network and on the insurance network.
It was found that this strategic decision to insure, as well as the mechanism by which the insurance network is formed, has the effect of endogenizing the quality of insurance. The latter is related to the risk that an insurer will fail to fulfill her obligation. This in turns affects the quantity of insurance that is demanded. Some counter-intuitive features predicted by this model include the fact that a suboptimal insurance network will tend to increase demand for insurance as a result of the presence of network effects.
The model provides insights into how to design mechanisms to control the formation of an insurance network so as to achieve a smaller and more effective one. It also provides an insurance-based argument to the enormous size of the credit-default swap (CDS) market, which supplements the current speculation-based arguments.
Matt Leduc, of Stanford University, California, is a citizen of Canada, resident in the United States. He was funded by IIASA's United States National Member Organization and worked in the Advanced Systems Analysis (ASA) Program during YSSP.
Please note these Proceedings have received limited or no review from supervisors and IIASA program directors, and the views and results expressed therein do not necessarily represent IIASA, its National Member Organizations, or other organizations supporting the work.
Last edited: 19 August 2015
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