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Optimal control of investment, premium and deductible for a non-life insurance company

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A risk-averse insurance company controls its reserve, modeled as a perturbed Cramér-Lundberg process, by choice of both the premium p and the deductible K offered to potential customers. The surplus is allocated to financial investment in a riskless and a basket of risky assets potentially correlating with the insurance risks and thus serving as a partial hedge against these. Assuming customers differ in riskiness, increasing p or K reduces the number of customers n(p,K) and increases the arrival rate of claims per customer λ(p,K) through adverse selection, with a combined negative effect on the aggregate arrival rate n(p,K)λ(p,K). We derive the optimal premium rate, deductible, investment strategy, and dividend payout rate (consumption by the owner-manager) maximizing expected discounted lifetime utility of intermediate consumption under the assumption of constant absolute risk aversion. Closed-form solutions are provided under specific assumptions on the distributions of size and frequency of claims.

OriginalsprogEngelsk
TidsskriftInsurance: Mathematics and Economics
Vol/bind101
NummerPart B
Sider (fra-til)384-405
Antal sider22
ISSN0167-6687
DOI
StatusUdgivet - nov. 2021

Bibliografisk note

Funding Information:
Bent Jesper Christensen and Juan Carlos Parra-Alvarez are also research fellows at the Danish Finance Institute (DFI), the Center for Research in Econometric Analysis of TimE Series (CREATES), and the Dale T. Mortensen Center (DTMC). Part of this research was done while Rafael Serrano was visiting Aarhus University, and he gratefully acknowledges financial support from DTMC . We are also grateful to the anonymous reviewers for helpful comments.

Funding Information:
Bent Jesper Christensen and Juan Carlos Parra-Alvarez are also research fellows at the Danish Finance Institute (DFI), the Center for Research in Econometric Analysis of TimE Series (CREATES), and the Dale T. Mortensen Center (DTMC). Part of this research was done while Rafael Serrano was visiting Aarhus University, and he gratefully acknowledges financial support from DTMC. We are also grateful to the anonymous reviewers for helpful comments.

Publisher Copyright:
© 2021 Elsevier B.V.

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