# Solvency capital requirement for a temporal dependent losses in insurance

*Sawssen Araichi*,
*Christian de Peretti* and
*Lotfi Belkacem*

*Economic Modelling*, 2016, vol. 58, issue C, pages 588-598

**Abstract:**
This article addresses the appropriate modeling of losses for the insurance sector. In fact, solvency 2 framework has suggested some formulas to evaluate losses and solvency capital using an internal approach. However, these formulas where derived under the assumption of independent losses. Thus, the amount of capital may be inaccurate when losses are dependent, which is the case in practice. The aim of this paper is to investigate temporal dependence structure among claim amounts (losses). For that, a novel model named autoregressive conditional amount (ACA) model handling the dynamic behavior of claim amounts in insurance companies is proposed. Results show that ACA models allow to predict accurately the future claims. Moreover, a measure of risk namely value at risk (VaR) ACA that could hedge daily dependent losses is provided. By backtesting techniques, empirical results show that the new VaR ACA can efficiently evaluate the coverage amount of risks.

**Keywords:** Claim amounts; Temporal dependence; Generalized extreme value model; Value at risk; Backtesting (search for similar items in EconPapers)

**JEL-codes:** C22 C23 C52 C58 G22 (search for similar items in EconPapers)

**Date:** 2016

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**Persistent link:** http://EconPapers.repec.org/RePEc:eee:ecmode:v:58:y:2016:i:c:p:588-598

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