Inference for heavy-tail models with financial applications

诸如大额索赔或利率变化等极端事件可能对保险和金融领域公司的盈利能力产生非常负面的影响。因此，必须利用适当的统计模型，适当评估这些事件发生的概率，以便更好地防范这些事件。通常，感兴趣的随机量不会产生从一个时间段到下一个时间段独立的值。从模型中排除这种依赖性可能会对应该为风险收取的适当保费产生很大的负面影响。在这个项目中，我们将研究各种长尾模型和相关风险模型，这些模型可用于精算和金融风险，并开发算法来估计这些模型的参数。

Extreme events such as large claims or changes in interest rates, could have a very negative  impact on the profitability of a company in the insurance and finance field. It is therefore important to evaluate properly the probability of occurence of those events, with the adequate statistical model, to better protect against them. Often, the random quantity of interest does not produce values which are independent from one time period to the next one. Leaving out this dependence from the model could have a large negative effect on the adequate premium which should be charged for the risk. In this project, we will look at various models with long tails and models for dependent risks which could be used for actuarial and financial risks and develop algorithms to estimate the parameters of those models.