A BSDE-based approach for the optimal reinsurance problem under partial information

M. Brachetta and C. Ceci

Insurance: Mathematics and Economics, 2020, vol. 95, issue C, 1-16

Abstract: We investigate the optimal reinsurance problem under the criterion of maximizing the expected utility of terminal wealth when the insurance company has restricted information on the loss process. We propose a risk model with claim arrival intensity and claim sizes distribution affected by an unobservable environmental stochastic factor. By filtering techniques (with marked point process observations), we reduce the original problem to an equivalent stochastic control problem under full information. Since the classical Hamilton–Jacobi–Bellman approach does not apply, due to the infinite dimensionality of the filter, we choose an alternative approach based on Backward Stochastic Differential Equations (BSDEs). Precisely, we characterize the value process and the optimal reinsurance strategy in terms of the unique solution to a BSDE driven by a marked point process.

Keywords: Optimal reinsurance; Partial information; Stochastic control; Stochastic factor risk models; Backward stochastic differential equations (search for similar items in EconPapers)
JEL-codes: C61 G22 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:95:y:2020:i:c:p:1-16

DOI: 10.1016/j.insmatheco.2020.07.009

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