This article studies the robust dividend, financing, and reinsurance strategies for an ambiguity aversion insurer (AAI) under model uncertainty. The AAI controls its liquid reserves by purchasing proportional reinsurance, paying dividends, and issuing new equity. We consider model uncertainty and suppose that the AAI is ambiguous about the liquid reserves process, which is described by a class of equivalent probability measures. The objective of the AAI is to maximize the expected present value of the dividend payouts minus the discounted costs of issuing new equity before bankruptcy under the worst-case scenario. A detailed proof of the verification theorem is shown for the robust singular-regular problem. We obtain the explicit solutions of the robust strategies, which are classified into three cases. Numerical results are also presented to show the impacts of the ambiguity aversion coefficient, and the transaction cost factor.

本文研究了模型不确定性下模糊厌恶保险公司 (AAI) 的稳健股息、融资和再保险策略。AAI 通过购买比例再保险、支付股息和发行新股来控制其流动储备。我们考虑模型不确定性，并假设 AAI 对液体储备过程不明确，该过程由一类等效概率度量来描述。AAI 的目标是在最坏的情况下，最大化股息支付的预期现值减去破产前发行新股的贴现成本。针对鲁棒奇异正则问题，给出了验证定理的详细证明。我们得到了鲁棒策略的显式解，分为三种情况。