Budget-constrained semi-dynamic optimal reinsurance strategies

Ka Chun Cheung; Xin Song; Yaodi Yong; Yiying Zhang; Ka Chun Cheung; Xin Song; Yaodi Yong; Yiying Zhang

doi:10.3934/jimo.2026181

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 10: 5247-5274. doi: 10.3934/jimo.2026181

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Research article

Budget-constrained semi-dynamic optimal reinsurance strategies

1.
Department of Statistics and Actuarial Science, School of Computing and Data Science, The University of Hong Kong, Pokfulam Road, Hong Kong, P.R. China
2.
Nankai-Taikang College of Insurance and Actuarial Science, Nankai University, Tianjin 300350, P.R. China
3.
Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, P.R. China

Received: 22 June 2026 Revised: 01 September 2026 Accepted: 09 September 2026 Published: 21 September 2026
91G05, 91G80

In this paper, we study a budget-constrained reinsurance problem under a semi-dynamic framework, where an insurer faces a random number of claims and seeks to maximize the expected utility of terminal wealth. The occurrence times of claims are incorporated through discounting, allowing the model to capture the time value. For independent claims, we prove the optimality of stop-loss reinsurance contracts for a risk-averse insurer under a premium budget constraint. In the risk-neutral case, we derive pairwise structural properties of the deductible allocation in terms of the claim severities and occurrence times. We find that assigning the larger of two deductible levels to a stochastically larger claim whose arrival time is smaller in the Laplace-transform order is weakly preferable. Additionally, we establish a comparison among deductible allocations via the majorization order. When claims are dependent but the exact dependence structure is unknown, we characterize the worst-case dependence structure as comonotonicity and also establish the optimality of stop-loss reinsurance contracts under this worst-case scenario. Numerical examples and comparative statics based on Monte Carlo simulation are provided to illustrate the theoretical results.
- budget constraint,
- optimal reinsurance,
- semi-dynamic,
- stop-loss,
- stochastic order,
- comonotonicity
Citation: Ka Chun Cheung, Xin Song, Yaodi Yong, Yiying Zhang. Budget-constrained semi-dynamic optimal reinsurance strategies[J]. Journal of Industrial and Management Optimization, 2026, 22(10): 5247-5274. doi: 10.3934/jimo.2026181

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Abstract

In this paper, we study a budget-constrained reinsurance problem under a semi-dynamic framework, where an insurer faces a random number of claims and seeks to maximize the expected utility of terminal wealth. The occurrence times of claims are incorporated through discounting, allowing the model to capture the time value. For independent claims, we prove the optimality of stop-loss reinsurance contracts for a risk-averse insurer under a premium budget constraint. In the risk-neutral case, we derive pairwise structural properties of the deductible allocation in terms of the claim severities and occurrence times. We find that assigning the larger of two deductible levels to a stochastically larger claim whose arrival time is smaller in the Laplace-transform order is weakly preferable. Additionally, we establish a comparison among deductible allocations via the majorization order. When claims are dependent but the exact dependence structure is unknown, we characterize the worst-case dependence structure as comonotonicity and also establish the optimality of stop-loss reinsurance contracts under this worst-case scenario. Numerical examples and comparative statics based on Monte Carlo simulation are provided to illustrate the theoretical results.

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