Nonparametric Estimation of the Finite-Time Survival Probability with Zero Initial Capital in the Classical Risk Model

作者：Qin Li; Pitts Susan M^*

来源：Methodology and Computing in Applied Probability, 2012, 14(4): 919-936.

DOI：10.1007/s11009-011-9212-4

• Finite-time survival probabilities
• Ruin time
• Functional central limit theorem
• Infinite-dimensional delta method
• Empirical processes
• Fast Fourier transform algorithm

In a classical risk model with zero initial capital and unknown claim-size distribution, we consider the statistical problem of estimating uniformly in t the (unknown) finite-time survival probability phi (0)(t) at time t, given a sample of claim sizes. We construct an empirical estimator of the function phi (0)(center dot) based on the sample of claim sizes, and using a functional approach we establish asymptotic statistical properties of our estimator with respect to supremum norm. We also consider numerical evaluation of finite-time survival probabilities and their empirical counterparts using the fast Fourier transform algorithm, and we carry out small-scale simulation studies of the behaviour of our estimator.

• 出版日期2012-12