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arXiv · 2401.08094

Optimal Insurance to Maximize Exponential Utility when Premium is Computed by a Convex Functional

Jingyi Cao·Dongchen Li·Virginia R. Young·Bin Zou
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Abstract

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.

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Jingyi Cao, Dongchen Li, Virginia R. Young, Bin Zou. 2024-01-16. Optimal Insurance to Maximize Exponential Utility when Premium is Computed by a Convex Functional. https://arxiv.org/abs/2401.08094

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