Optimal control of investment, premium and deductible for a non-life insurance company
| Autor: | Rafael Serrano, Bent Jesper Christensen, Juan Carlos Parra-Alvarez |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Consumption (economics) Economics and Econometrics Adverse selection Investment strategy Dividend payout ratio Investment (macroeconomics) Deductible Stochastic optimal control Premium control Life insurance Optimal investment strategy Econometrics Economics Statistics Probability and Uncertainty Deductible control Hedge (finance) Jump-diffusion Hamilton-Jacobi-Bellman equation |
| Zdroj: | Aarhus University Christensen, B J, Parra-Alvarez, J C & Serrano, R 2021, ' Optimal control of investment, premium and deductible for a non-life insurance company ', Insurance: Mathematics and Economics, vol. 101, no. Part B, pp. 384-405 . https://doi.org/10.1016/j.insmatheco.2021.07.005 |
| ISSN: | 0167-6687 |
| DOI: | 10.1016/j.insmatheco.2021.07.005 |
| Popis: | A risk-averse insurance company controls its reserve, modeled as a perturbed Cramer-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. |
| Databáze: | OpenAIRE |
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