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Optimal proportional reinsurance to maximize an insurer’s exponential utility under unobservable drift

Part of: Stochastic systems and control Existence theories Stochastic processes

Published online by Cambridge University Press:  21 February 2023

Xiaoqing Liang Open the ORCID record for Xiaoqing Liang [Opens in a new window]  and
Virginia R. Young
Xiaoqing Liang*
Affiliation:
Hebei University of Technology
Virginia R. Young*
Affiliation:
University of Michigan
*
*Postal address: Departmnt of Statistics, School of Sciences, Hebei University of Technology, Tianjin 300401, P. R. China. Email: liangxiaoqing115@hotmail.com
**Postal address: Department of Mathematics, University of Michigan, Ann Arbor, Michigan, 48109. Email: vryoung@umich.edu
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Abstract

We study an optimal reinsurance problem for a diffusion model, in which the drift of the claim follows an Ornstein–Uhlenbeck process. The aim of the insurer is to maximize the expected exponential utility of its terminal wealth. We consider two cases: full information and partial information. Full information occurs when the insurer directly observes the drift; partial information occurs when the insurer observes only its claims. By applying stochastic control and by solving the corresponding Hamilton–Jacobi–Bellman equations, we find the value function and the optimal reinsurance strategy under both full and partial information. We determine a relationship between the value function and reinsurance strategy under full information with the value function and reinsurance strategy under partial information.

Keywords

Exponential utilitymean-reverting driftincomplete informationoptimal reinsurance

MSC classification

Primary: 93E20: Optimal stochastic control 93E11: Filtering
Secondary: 49J40: Variational methods including variational inequalities 60G15: Gaussian processes
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 3 , September 2023 , pp. 874 - 894
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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