Markov链利率下再保险模型的破产概率上界

摘要

Upper bounds for the ruin probability of reinsurance were studied in a discrete time risk model.To reduce the risk,there is a possibility to reinsure a part or the whole reserve.In the model,the time between the occurrence of the claims and the claims were assumed to be the AR(1)structure,the interest rates followed a Markov chain with a denumerable state space.The risk model of proportional reinsurance was considered.The upper bounds for the ruin probability were derived both by renewal recursive technique and martingale method.As an important indicator of the abilities of solvency and risk manage-ment,the research of the ruin probability can provide an important basis for reinsurer's major decisions,so it has important the-oretical and practical significance.%研究了如何确定离散时间情况下再保险模型破产概率上界的问题。为了降低自身的破产风险，保险公司常常对部分乃至全部资产进行再保险。假定索赔间隔时间和索赔额具有一阶自回归结构，假定利率过程为取值于可数状态空间的 Markov链。建立了其比例再保险模型，分别用递归更新技巧和鞅方法得到模型的破产概率上界。该破产概率上界作为评估再保险公司偿付能力和风险控制能力的重要指标，对于它的研究成果能为再保险人做出重大决策提供重要的依据，具有较为重要的理论和现实意义。