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

Bent Jesper Christensen, Juan Parra-Alvarez and Rafael Serrano ()

Insurance: Mathematics and Economics, 2021, vol. 101, issue PB, 384-405

Abstract: 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.

Keywords: Stochastic optimal control; Hamilton-Jacobi-Bellman equation; Jump-diffusion; Adverse selection; Premium control; Deductible control; Optimal investment strategy (search for similar items in EconPapers)
JEL-codes: C60 D82 G11 G22 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Working Paper: Optimal control of investment, premium and deductible for a non-life insurance company (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:101:y:2021:i:pb:p:384-405

DOI: 10.1016/j.insmatheco.2021.07.005

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