考虑投资回报的相依离散风险模型的破产概率  

Ruin probability for a discrete time model with investment returns and dependent structure

作　　者：殷明娥[1] 牛祥秋 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2017年第4期451-455,共5页Journal of Liaoning Normal University:Natural Science Edition

摘　　要：破产概率是保险公司度量风险的重要手段,而计算破产概率也是经典风险理论中最为核心的问题之一.相对于破产概率的精确表达式,保险公司可能更关心通过再保险及投资等方式,使得破产概率尽可能小.研究一类含有投资回报的相依离散时间风险模型,模型中假设持续的投入资金量是常数形式,并且假设股票市场的回报比例和净损失均具有一阶自回归结构,而利率为一个马尔科夫链.通过构造一个上鞅,利用最优停时定理给出了破产概率的上界估计.Ruin probability is an important tool for insurance companies to measure risks,and the calculation of ruin probability is also one of the core issues in classical risk theory.Compared to the exact expression of ruin probability,the insurance company may be more concerned to minimize the ruin probability through reinsurance and investments.We study a class of dependent discrete time risk model with investment returns,in which the amount of investment is assumed to be a constant and the stock market returns ratio and net losses follow autoregressive structures of order one,while the interest rate is a Markov chain.By constructing a martingale,upper bound for ruin probability is obtained by using the optimal stopping theorem.

关 键 词：一阶自回归 马尔科夫链 破产概率 

分 类 号：O211.6[理学—概率论与数理统计]