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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.
Original language | English |
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Journal | Insurance: Mathematics and Economics |
Volume | 101 |
Issue | Part B |
Pages (from-to) | 384-405 |
Number of pages | 22 |
ISSN | 0167-6687 |
DOIs | |
Publication status | Published - Nov 2021 |
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© 2021 Elsevier B.V.
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ID: 226702859