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A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

Published online by Cambridge University Press:  09 August 2013

Benjamin Baumgartner  and
Riccardo Gatto
Benjamin Baumgartner
Affiliation:
Institute of Mathematical Statistics and Actuarial Science, University of Bern, Alpeneggstrasse 22, 3012 Bern, Switzerland, E-mail: [email protected], E-mail: [email protected]
Riccardo Gatto
Affiliation:
Institute of Mathematical Statistics and Actuarial Science, University of Bern, Alpeneggstrasse 22, 3012 Bern, Switzerland, E-mail: [email protected], E-mail: [email protected]
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Abstract

In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process. We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone. We provide second-order accurate P-values for this testing problem and consider both parametric and nonparametric estimators of the individual claim amount distribution. Simulation studies show that the suggested bootstrap P-values are very accurate and outperform their analogues based on the asymptotic normal approximation.

Keywords

Edgeworth expansionexponential and log-normal claim amountsnormal approximationP-valuepivotal quantityresamplingsecond-order accuracy
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 241 - 255
Copyright
Copyright © International Actuarial Association 2010

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