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The academic community should be indebted to Professors Jun Cai and Yichun Chi for their meticulously written review paper (referred to as Cai & Chi, in press in what follows) on optimal reinsurance, which summarises and synthesises the historical developments and recent advances in this burgeoning research field. In the current era, where risk management has found more and more applications, this review paper cannot be more timely and will definitely provide the impetus for future research in this and broader areas.

In keeping with Cai and Chi (in press)’s notation and terminology, this discussion aims to complement their review paper by highlighting an important line of recent research and its prospective future directions: The study of risk-measure-based optimal reinsurance contracts with practical constraints. Given an objective functional (a notable example being a distortion risk measure; see Section 5 of …