This paper studies an optimal reinsurance, investment, and prevention problem for an insurer under common shock dependence. The aggregate loss consists of two claim streams with independent claim sizes and dependent claim arrivals driven by a common shock component. The insurer chooses reinsurance, investment, and prevention to maximize the expected utility of terminal wealth, where prevention lowers the arrival intensities at a convex cost. Reinsurance is modeled in a general admissible framework without imposing a specific contract form. Under exponential utility, we derive the Hamilton-Jacobi-Bellman equation and establish a verification theorem. The optimal investment strategy is explicit, the optimal reinsurance policy is shown to be of the excess-of-loss type, and the optimal prevention strategy can be expressed using the inverse marginal cost function. Numerical results further demonstrate the value of prevention and show how prevention effectiveness, prevention cost, and risk aversion affect the optimal strategies.
Citation: Rong Hu, Xin Zhang. Optimal reinsurance–investment with prevention under common-shock dependence[J]. Electronic Research Archive, 2026, 34(9): 6877-6904. doi: 10.3934/era.2026299
This paper studies an optimal reinsurance, investment, and prevention problem for an insurer under common shock dependence. The aggregate loss consists of two claim streams with independent claim sizes and dependent claim arrivals driven by a common shock component. The insurer chooses reinsurance, investment, and prevention to maximize the expected utility of terminal wealth, where prevention lowers the arrival intensities at a convex cost. Reinsurance is modeled in a general admissible framework without imposing a specific contract form. Under exponential utility, we derive the Hamilton-Jacobi-Bellman equation and establish a verification theorem. The optimal investment strategy is explicit, the optimal reinsurance policy is shown to be of the excess-of-loss type, and the optimal prevention strategy can be expressed using the inverse marginal cost function. Numerical results further demonstrate the value of prevention and show how prevention effectiveness, prevention cost, and risk aversion affect the optimal strategies.
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Rong Hu, Xin Zhang. Optimal reinsurance–investment with prevention under common-shock dependence[J]. Electronic Research Archive, 2026, 34(9): 6877-6904. doi: 10.3934/era.2026299
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