Optimal Insurance to Maximize Exponential Utility when Premium is Computed by a Convex Functional
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929210460733440 |
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| author | Cao, Jingyi Li, Dongchen Young, Virginia R. Zou, Bin |
| author_facet | Cao, Jingyi Li, Dongchen Young, Virginia R. Zou, Bin |
| contents | We find the optimal indemnity to maximize the expected utility of terminal wealth of a buyer of insurance whose preferences are modeled by an exponential utility. The insurance premium is computed by a convex functional. We obtain a necessary condition for the optimal indemnity; then, because the candidate optimal indemnity is given implicitly, we use that necessary condition to develop a numerical algorithm to compute it. We prove that the numerical algorithm converges to a unique indemnity that, indeed, equals the optimal policy. We also illustrate our results with numerical examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_08094 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Insurance to Maximize Exponential Utility when Premium is Computed by a Convex Functional Cao, Jingyi Li, Dongchen Young, Virginia R. Zou, Bin Mathematical Finance Optimization and Control Risk Management 91G05, 93E20, 49M05 We find the optimal indemnity to maximize the expected utility of terminal wealth of a buyer of insurance whose preferences are modeled by an exponential utility. The insurance premium is computed by a convex functional. We obtain a necessary condition for the optimal indemnity; then, because the candidate optimal indemnity is given implicitly, we use that necessary condition to develop a numerical algorithm to compute it. We prove that the numerical algorithm converges to a unique indemnity that, indeed, equals the optimal policy. We also illustrate our results with numerical examples. |
| title | Optimal Insurance to Maximize Exponential Utility when Premium is Computed by a Convex Functional |
| topic | Mathematical Finance Optimization and Control Risk Management 91G05, 93E20, 49M05 |
| url | https://arxiv.org/abs/2401.08094 |