The paper provides a comprehensive overview of modeling and pricing cyber insurance and includes clear and easily understandable explanations of the underlying mathematical concepts. We distinguish three main types of cyber risks: idiosyncratic, systematic, and systemic cyber risks. While for idiosyncratic and systematic cyber risks, classical actuarial and financial mathematics appear to be well-suited, systemic cyber risks require more sophisticated approaches that capture both network and strategic interactions. In the context of pricing cyber insurance policies, issues of interdependence arise for both systematic and systemic cyber risks; classical actuarial valuation needs to be extended to include more complex methods, such as concepts of risk-neutral valuation and (set-valued) monetary risk measures.
We study the ex-ante maximization of market efficiency, defined in terms of minimum deviation of market prices from fundamental values, from a centralized planner's perspective. Prices are pressured from exogenous trading actions of leverage targeting banks, which rebalance their portfolios in response to asset shocks. We develop an explicit expression for the matrix of asset holdings which minimizes market inefficiency, and characterize it in terms of two key sufficient statistics: the banks' systemic significance and the statistical moments of asset shocks. Our analysis shows that higher homogeneity in banks' systemic significance requires banks' portfolio holdings to be further away from a full diversification strategy to reduce inefficiencies.
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