# Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes

*Stéphane Loisel* (),
*Christian Mazza* and
*Didier Rulliere* ()

*Insurance: Mathematics and Economics*, 2009, vol. 45, issue 3, 374-381

**Abstract:**
In the classical risk model, we prove the weak convergence of a sequence of empirical finite-time ruin probabilities. In an earlier paper (see Loisel etÂ al., (2008)), we proved an equivalent result in the special case where the initial reserve is zero, and checked that numerically the general case seems to be true. In this paper, we prove the general case (with a nonnegative initial reserve), which is important for applications to estimation risk. So-called partly shifted risk processes are introduced, and used to derive an explicit expression of the asymptotic variance of the considered estimator. This provides a clear representation of the influence function associated with finite time ruin probabilities and gives a useful tool to quantify estimation risk according to new regulations.

**Keywords:** Finite-time; ruin; probability; Robustness; Solvency; II; Reliable; ruin; probability; Asymptotic; normality; Influence; function; Estimation; Risk; Solvency; Margin; (ERSM); Partly; shifted; risk; process (search for similar items in EconPapers)

**Date:** 2009

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**Related works:**

Working Paper: Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes (2009)

Working Paper: Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes (2007)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:insuma:v:45:y:2009:i:3:p:374-381

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