Inference for heavy-tail models with financial applications

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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.