论文标题
通过Malliavin微积分估计剩余的有限时间毁灭概率
Estimating the finite-time ruin probability of a surplus with a long memory via Malliavin calculus
论文作者
论文摘要
我们考虑了带有赫斯特指数$ h> 1/2 $的漂移分数布朗运动的盈余过程，该过程似乎是带有相关主张的漂移复合泊松风险模型的功能限制，这是一种长期记忆的盈余表示。我们的兴趣是构建剩余损失概率的置信区间，当时波动率参数尚不清楚。我们将获得毁灭概率W.R.T.的派生。通过malliavin conculus的挥发性参数，并应用Delta方法来识别估计的破坏概率的渐近分布。
We consider a surplus process of drifted fractional Brownian motion with the Hurst index $H>1/2$, which appears as a functional limit of drifted compound Poisson risk models with correlated claims, and this is a kind of representation of a surplus with a long memory. Our interest is to construct confidence intervals of the ruin probability of the surplus when the volatility parameter is unknown. We will obtain the derivative of the ruin probability w.r.t. the volatility parameter via Malliavin calculus, and apply the delta method to identify the asymptotic distribution of an estimated ruin probability.
