Optimal Reinsurance Revisited – A Geometric Approach

By Ka Chun Cheung. ASTIN Bulletin: The Journal of the International Actuarial Association, 2010

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Optimal reinsurance designs based on risk measures: a review (2020, methodology): “the insurer, as observed by Cheung and Lo (2017). Noting that f ′(t) ∈ [0, 1] for any f ∈ C2, it easily follows from the above equation that”
Optimal reinsurance with expectile (2016, unknown): “See, for instance, Gajek & Zagrodny (2004), Huang (2006), Balbás et al. (2009), Young (1999), Cheung (2010), Asimit et al. (2013c), Chi & Meng (2013), Cheung et al. (2014b), and so on.”
Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles (2013, unknown): “(9) Here 0 ≤ ai, bi ≤ 1 are arbitrary constants, the points {q+ r,g(i), q− r,g(i); i = 1, · · · , n (1) r,g} and {q̂+ r,g(i), q̂− r,g(i); i = 1, · · · , n (2) r,g} are given by equation (5), and {tr,g(i), tr,g(i); i = 1, · · · ,m((1)) r,g} and {t̂r,g(i), t̂r,g(i); i = 1, · · · ,m (2) r,g} are given ”
Optimal Reinsurance with General Premium Principles (2013, unknown): “Moreover, C strictly contains the set of increasing convex ceded loss functions over which the optimal reinsurance problems are studied in Cai et al. (2008) and Cheung (2010).”