Solvency capital requirement for a temporal dependent losses in insurance

- Losses in insurance present a dynamic behaviour.
- The novel ACA models predict adequately the future losses.
- The novel specication of GEV captures autocorrelations between large losses.
- The solvency capital provides a prompt hedge of risks.
- Results may be applied on any financial loss problem.

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.