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

Li Qin and Susan M. Pitts ()
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Li Qin: University of Cambridge
Susan M. Pitts: University of Cambridge

Methodology and Computing in Applied Probability, 2012, vol. 14, issue 4, 919-936

Abstract: Abstract 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 φ 0(t) at time t, given a sample of claim sizes. We construct an empirical estimator of the function φ 0(·) 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.

Keywords: Finite-time survival probabilities; Ruin time; Functional central limit theorem; Infinite-dimensional delta method; Empirical processes; Fast Fourier transform algorithm; 62G05; 62G20; 91B30 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-011-9212-4

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