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Évaluation Et Allocation Du Risque Dans Le Cadre De Modèles Avancés En Actuariat
| Content Provider | Semantic Scholar |
|---|---|
| Author | Moutanabbir, Khouzeima |
| Copyright Year | 2013 |
| Abstract | In this thesis, we are interested in risk evaluation and risk allocation problems using advanced actuarial models. First, we investigate risk aggregation and capital allocation problems for a portfolio of possibly dependent risks whose multivariate distribution is defined with the Farlie-Gumbel-Morgenstern copula and with mixed Erlang distributions for the marginals. In such a context, we first show that the aggregate claim amount has a mixed Erlang distribution. Based on a top-down approach, closed-form expressions for the contribution of each risk are derived using the TVaR and covariance rules. These findings are illustrated with numerical examples. Then, we propose to investigate the distribution of the discounted sum of ascending ladder heights over finiteor infinite-time intervals within the Sparre Andersen risk model. In particular, the moments of the discounted sum of ascending ladder heights over a finiteand an infinite-time intervals are derived in both the classical compound Poisson risk model and the Sparre Andersen risk model with exponential claims. The application of a particular Gerber-Shiu functional is central to the derivation of these results, as is the mixed Erlang distributional assumption. Finally, we define VaR and TVaR risk measures in terms of the discounted sum of ascending ladder heights. We use a moment-matching method to approximate the distribution of the discounted sum of ascending ladder heights allowing the computation of the VaR and TVaR risk measures. In the last chapter, we present a stochastic investment model (SIM) for international investors. We assume that investors are allowed to hold assets in two different economies. This SIM includes four components: interest rates, stocks, inflation and exchange rate models. First, we give a full description of the model and we detail the parameter estimation. The model is estimated using a state-space formulation and an extended Kalman filter. Based on scenarios generated from this SIM, we study the risk allocation to different background risks: asset, inflation and exchange rate risks. The risk allocation is based on the TVaR-based rule. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://corpus.ulaval.ca/jspui/bitstream/20.500.11794/24031/1/29730.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
