阈值分红策略下的相依对偶风险模型

Dependent Dual Risk Model under Threshold Dividend Strategy

摘要: 本文研究了一类相依对偶风险模型，其中相依结构由Copula函数确定，在模型中我们引入阈值分红策略，当盈余超过阈值b时，超额部分将作为红利立即支付给股东，小于b时不支付红利；以股息预期贴现值和破产概率为研究对象，得到了它们满足的微积分方程，当索赔服从指数分布时，得到了破产概率的解析表达式；最后，为验证理论结果的有效性，对理论结果做了数值模拟，选取不同相依参数与初始盈余水平，分析二者对破产概率的影响规律。

Abstract: This paper studies a class of dependent dual risk models where the dependence structure is determined by a Copula function. A threshold dividend strategy is introduced in the model: when the surplus exceeds the threshold b, the excess part is immediately paid to shareholders as dividends; no dividends are paid when the surplus is less than b. Focusing on the expected discounted value of dividends and the ruin probability, the differential-integral equations they satisfy are derived. When the claims follow an exponential distribution, the analytical expression of the ruin probability is obtained. Finally, to verify the validity of the theoretical results, numerical simulations are conducted. Different dependence parameters and initial surplus levels are selected to analyze the influence patterns of both on the ruin probability.