Optimal Reinsurance Problem under Fixed Cost and Exponential Preferences

Matteo Brachetta and Claudia Ceci
Additional contact information
Matteo Brachetta: Department of Mathematics, Politecnico of Milan, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy
Claudia Ceci: Department of Economics, University of Chieti-Pescara, Viale Pindaro, 42, 65127 Pescara, Italy

Mathematics, 2021, vol. 9, issue 4, 1-20

Abstract: We investigate an optimal reinsurance problem for an insurance company taking into account subscription costs: that is, a constant fixed cost is paid when the reinsurance contract is signed. Differently from the classical reinsurance problem, where the insurer has to choose an optimal retention level according to some given criterion, in this paper, the insurer needs to optimally choose both the starting time of the reinsurance contract and the retention level to apply. The criterion is the maximization of the insurer’s expected utility of terminal wealth. This leads to a mixed optimal control/optimal stopping time problem, which is solved by a two-step procedure: first considering the pure-reinsurance stochastic control problem and next discussing a time-inhomogeneous optimal stopping problem with discontinuous reward. Using the classical Cramér–Lundberg approximation risk model, we prove that the optimal strategy is deterministic and depends on the model parameters. In particular, we show that there exists a maximum fixed cost that the insurer is willing to pay for the contract activation. Finally, we provide some economical interpretations and numerical simulations.

Keywords: optimal reinsurance; mixed control problem; optimal stopping; transaction cost (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/4/295/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/4/295/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:4:p:295-:d:492139

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().