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Optimal insurance with counterparty and additive background risk

Published online by Cambridge University Press:  02 February 2024

Yanhong Chen Open the ORCID record for Yanhong Chen [Opens in a new window]
Yanhong Chen*
Affiliation:
College of Finance and Statistics, Hunan University, Changsha 410082, P.R. China
*
Email: yhchen@hnu.edu.cn
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Abstract

In this paper, we explore how to design the optimal insurance contracts when the insured faces insurable, counterparty, and additive background risk simultaneously. The target is to minimize the mean-variance of the insured’s loss. By utilizing the calculus of variations, an implicit characterization of the optimal ceded loss function is given. An explicit structure of the optimal ceded loss function is also provided by making full use of its implicit characterization. We further derive a much simpler solution when these three kinds of risk have some special dependence structures. Finally, we give a numerical example to illustrate our results.

Keywords

Optimal insurancecounterparty riskbackground riskmean-variance optimizationC61G22G32
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 54 , Issue 2 , May 2024 , pp. 441 - 462
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The International Actuarial Association

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