Optimal reinsurance via BSDEs in a partially observable model with jump clusters

Matteo Brachetta (), Giorgia Callegaro (), Claudia Ceci () and Carlo Sgarra ()
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Matteo Brachetta: Politecnico di Milano
Giorgia Callegaro: University of Padova
Claudia Ceci: University of Rome La Sapienza
Carlo Sgarra: Università di Bari

Finance and Stochastics, 2024, vol. 28, issue 2, No 5, 453-495

Abstract: Abstract We investigate an optimal reinsurance problem when the loss process exhibits jump clustering features and the insurance company has restricted information about the loss process. We maximise expected exponential utility of terminal wealth and show that an optimal strategy exists. By exploiting both the Kushner–Stratonovich and Zakai approaches, we provide the equation governing the dynamics of the (infinite-dimensional) filter and characterise the solution of the stochastic optimisation problem in terms of a BSDE, for which we prove existence and uniqueness of a solution. After discussing the optimal strategy for a general reinsurance premium, we provide more explicit results in some relevant cases.

Keywords: Optimal reinsurance; Partial information; Hawkes processes; Cox processes with shot noise; BSDEs; 93E20; 91B30; 60G40; 60J60 (search for similar items in EconPapers)
JEL-codes: C61 G11 G22 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00780-023-00523-z

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