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

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  • Li Qin

    (University of Cambridge)

  • Susan M. Pitts

    (University of Cambridge)

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.

Suggested Citation

  • Li Qin & Susan M. Pitts, 2012. "Nonparametric Estimation of the Finite-Time Survival Probability with Zero Initial Capital in the Classical Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 919-936, December.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:4:d:10.1007_s11009-011-9212-4
    DOI: 10.1007/s11009-011-9212-4
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    References listed on IDEAS

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