Model uncertainty is ubiquitous and plays an important role in insurance and financial modeling. While a substantial effort has been given to studying optimal consumption, portfolio selection and investment problems in the presence of model uncertainty, relatively little attention is given to investigating optimal payout policies taking account of the impacts of model uncertainty. As one of the early attempts, this paper studies the optimal payout control problem under the classical risk model taking into account of model uncertainty about the claims arrival intensity. We aim to provide insights into understanding optimal decisions incorporating model uncertainty and to examine key impact of model uncertainty. We find that the optimal strategy robust to model uncertainty is of a band type. However, the presence of the model uncertainty alters the qualitative behavior of the optimal strategy in the sense that the optimal robust policy is no longer a barrier strategy for some particular cases. We provide numerical examples to illustrate the theoretical results and examine the impact of model uncertainty on optimal policies. We also provide examples that use real insurance data for calibration. We discover that the decision maker takes more conservative strategies under model uncertainty, which is consistent with the findings in the economic field and has not been addressed in the existing optimal payout problems without model uncertainty.

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Bruno de Finetti 满足模型不确定性时的最佳支付策略

模型不确定性无处不在，在保险和金融建模中发挥着重要作用。虽然人们在模型不确定性存在的情况下研究最优消费、投资组合选择和投资问题做出了大量努力，但相对较少的关注是研究考虑模型不确定性影响的最优支付政策。作为早期尝试之一，本文研究了考虑索赔到达强度模型不确定性的经典风险模型下的最优赔付控制问题。我们的目标是提供见解，帮助理解包含模型不确定性的最佳决策，并检查模型不确定性的关键影响。我们发现对不确定性建模具有鲁棒性的最佳策略是带状策略。然而，模型不确定性的存在改变了最优策略的定性行为，即最优鲁棒策略不再是某些特定情况下的障碍策略。我们提供数值示例来说明理论结果并检验模型不确定性对最优政策的影响。我们还提供了使用真实保险数据进行校准的示例。我们发现决策者在模型不确定性下采取更加保守的策略，这与经济领域的研究结果一致，并且在现有的无模型不确定性的最优支付问题中尚未得到解决。