一类两险种双Cox风险过程的破产概率估计

An Estimate of Ruin Probability for Double Cox and Two-Type-Risk insurance Risk Process

经典风险模型描述了单一险种且保费率是常数的经营模式。事实上保险公司经营是复杂的,险种是多元化的。考虑保费的到达和理赔的发生都服从Cox过程的两险种的风险模型,运用鞅论的方法,给出初始资本为u时破产概率Ψ(u)的明确表达式和其上界估计,以及累积强度相同且理赔额服从指数分布时的两险种双Cox风险模型的破产概率Ψ(u)的表达式。

Classical risk models for insurance are single-type based, and the rate of premium is constant. However, insurance companies actually use multiple-type-risk in practice. Considering a double Cox and two-type-risk insurance risk process where the amounts of claims and the arrivals of premium follow Cox process, the explicit expression of ruin probability ψ（u） and its upper bounds are obtained by using martingale, specially when the means of Cox processes are same and the claims obey exponential distribution.