The aim of the paper is to model ambiguity in a randomized reinsurance stop-loss treaty. For this, we consider the lower envelope of the set of bivariate joint probability distributions having a precise discrete marginal and an ambiguous Bernoulli marginal. Under an independence assumption, since the lower envelope fails 2-monotonicity, inner/outer Dempster-Shafer approximations are considered, so as to select the optimal retention level by maximizing the lower expected insurer's annual profit under reinsurance. We show that the inner approximation is not suitable in the reinsurance problem, while the outer approximation preserves the given marginal information, weakens the independence assumption, and does not introduce spurious information in the retention level selection problem. Finally, we provide a characterization of the optimal retention level.

Addressing ambiguity in randomized reinsurance stop-loss treaties using belief functions / Petturiti, Davide; Stabile, Gabriele; Vantaggi, Barbara. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - 161:(2023). [10.1016/j.ijar.2023.108986]

Addressing ambiguity in randomized reinsurance stop-loss treaties using belief functions

Stabile, Gabriele;Vantaggi, Barbara
2023

Abstract

The aim of the paper is to model ambiguity in a randomized reinsurance stop-loss treaty. For this, we consider the lower envelope of the set of bivariate joint probability distributions having a precise discrete marginal and an ambiguous Bernoulli marginal. Under an independence assumption, since the lower envelope fails 2-monotonicity, inner/outer Dempster-Shafer approximations are considered, so as to select the optimal retention level by maximizing the lower expected insurer's annual profit under reinsurance. We show that the inner approximation is not suitable in the reinsurance problem, while the outer approximation preserves the given marginal information, weakens the independence assumption, and does not introduce spurious information in the retention level selection problem. Finally, we provide a characterization of the optimal retention level.
2023
belief function; dempster-shafer approximation; reinsurance; stop-loss treaty
01 Pubblicazione su rivista::01a Articolo in rivista
Addressing ambiguity in randomized reinsurance stop-loss treaties using belief functions / Petturiti, Davide; Stabile, Gabriele; Vantaggi, Barbara. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - 161:(2023). [10.1016/j.ijar.2023.108986]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1686643
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