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THE EFFICIENT COMPUTATION AND THE SENSITIVITY ANALYSIS OF FINITE-TIME RUIN PROBABILITIES AND THE ESTIMATION OF RISK-BASED REGULATORY CAPITAL

Published online by Cambridge University Press:  03 March 2016

Mark S. Joshi  and
Dan Zhu
Mark S. Joshi*
Affiliation:
Department of Economics, University of Melbourne, Level 4/111 Barry Street Carlton, VIC 3053, Australia
Dan Zhu
Affiliation:
Department of Econometrics and Business Statistics, Monash University, Building H, 900 Dandenong Road, Caulfield East, Victoria 3145, Australia E-Mail: danzhu918@gmail.com
*
E-Mail: mark.joshi@gmail.com
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Abstract

Solvency regulations require financial institutions to hold initial capital so that ruin is a rare event. An important practical problem is to estimate the regulatory capital so the ruin probability is at the regulatory level, typically with less than 0.1% over a finite-time horizon. Estimating probabilities of rare events is challenging, since naive estimations via direct simulations of the surplus process is not feasible. In this paper, we present a stratified sampling algorithm for estimating finite-time ruin probabilities. We further introduce a sequence of measure changes to remove the pathwise discontinuities of the estimator, and compute unbiased first and second-order derivative estimates of the finite-time ruin probabilities with respect to both distributional and structural parameters. We then estimate the regulatory capital and its sensitivities. These estimates provide information to insurance companies for meeting prudential regulations as well as designing risk management strategies. Numerical examples are presented for the classical model, the Sparre Andersen model with interest and the periodic risk model with interest to demonstrate the speed and efficacy of our methodology.

Keywords

Sensitivity analysisruin probabilitiesMonte Carlorisk-based capital
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 46 , Issue 2 , May 2016 , pp. 431 - 467
Copyright
Copyright © Astin Bulletin 2016 

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