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Confidence bounds for the adjustment coefficient

Part of: Applications Nonparametric inference

Published online by Cambridge University Press:  01 July 2016

Susan M. Pitts ,
Rudolf Grübel  and
Paul Embrechts
Susan M. Pitts*
Affiliation:
University College London
Rudolf Grübel*
Affiliation:
Universität Hannover
Paul Embrechts*
Affiliation:
ETH, Zürich
*
∗ Postal address: Department of Statistical Science, University College London, Gower Street, London WCIE 6BT, UK.
∗∗ Postal address: Institut für Mathematische Stochastik, Universität Hannover, Postfach 6009, 30060 Hannover, Germany.
∗∗∗ Postal address: Department of Mathematics, ETH-Zentrum, CH-8092 Zürich, Switzerland.
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Abstract

Let ?(u) be the probability of eventual ruin in the classical Sparre Andersen model of risk theory if the initial risk reserve is u. For a large class of such models ?(u) behaves asymptotically like a multiple of exp (–Ru) where R is the adjustment coefficient; R depends on the premium income rate, the claim size distribution and the distribution of the time between claim arrivals. Estimation of R has been considered by many authors. In the present paper we deal with confidence bounds for R. A variety of methods is used, including jackknife estimation of asymptotic variances and the bootstrap. We show that, under certain assumptions, these procedures result in interval estimates that have asymptotically the correct coverage probabilities. We also give the results of a simulation study that compares the different techniques in some particular cases.

Keywords

RISK THEORYRUIN PROBABILITYADJUSTMENT COEFFICIENTRANDOM WALKNON-PARAMETRIC ESTIMATIONBOOTSTRAPJACKKNIFEBIAS CORRECTION

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 62G20: Asymptotic properties
Type
General Applied Probablity
Information
Advances in Applied Probability , Volume 28 , Issue 3 , September 1996 , pp. 802 - 827
Copyright
Copyright © Applied Probability Trust 1996 

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