L'approccio di B. De Finetti per la riassicurazione individuale proporzionale. Modelli semplificati e considerazioni operative

Mean–variance efficient strategies in proportional reinsurance under group correlation in a gaussian framework

“…This problem was originally raised by de Finetti in his path-breaking paper [9]; there, he gave a quick hint to some key properties of the solution but without giving closed form formulae. A subsequent treatment of this issue may be found in a paper by Gigante [16]; she was able to apply the Karush-Kuhn-Tucker conditions to the constrained quadratic optimization problem arising from the mean-variance approach to proportional reinsurance. This way she showed that, under group correlation, a fast version of the critical line algorithm could be applied to obtain rather quickly the whole mean-variance set of efficient retentions.…”

“…At our knowledge, the only subsequent treatment of this issue may be found in a paper by Gigante [16]. Recognizing the strict connection between the proportional reinsurance problem and the portfolio selection problem, early signalled by Pressacco [28], she applied the Karush-Kuhn-Tucker conditions ( [19], [20]) to the constrained quadratic optimization problem arising from the mean-variance approach to proportional reinsurance.…”

“…As said in the introduction, fifty years later Gigante [16] applied the KKT conditions to the constrained quadratic optimization problem arising from the application of the mean-variance approach to proportional reinsurance under group correlation. This way, she obtained a fast version of the critical line algorithm to get, through a sequential procedure (and not in closed form), the whole set of the mean-variance efficient retentions.…”