The regulator is interested in proposing a capital adequacy test by specifying an acceptance set for firms' capital positions at the end of a given period. This set needs to be surplus-invariant, i.e., not to depend on the surplus of firms' shareholders, because the test means to protect firms'...

Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem...

Risk measures are used not only for financial institutions’ internal risk management but also for external regulation (e.g., in the Basel Accord for calculating the regulatory capital requirements for financial institutions). Though fundamental in risk management, how to select a good risk...

This paper studies the design of Pareto-optimal reinsurance contracts in a market where the insurer and reinsurer maximize their expected utilities of end-of-period wealth. In addition, we assume that the insurer and reinsurer wish to control their solvency risks, which are defined through...

This paper unifies the work on multiple reinsurers, distortion risk measures, premium budgets,and heterogeneous beliefs. An insurer minimizes a distortion risk measure, while seekingreinsurance with finitely many reinsurers. The reinsurers use distortion premium principles, andthey are allowed...