This thesis studies two new approaches of risk measurement. The first one is based on the class of spectral risk measures and proposes a new method to calibrate them to data and decision maker's objective. Based on the results of information theory, we use theorems of relative entropy optimisation to build a framework which allows data-specific calibration and selection of the best spectral risk measure among several candidates. The calibration procedure ensures that an optimal risk aversion coefficient is attained with respect to a constraint on the rst moment of the data distribution. The selection procedure provides an indication on which risk spectrum should be used in order to maximize the likelihood of the decision maker's objective, thus her risk aversion. Application to real data are then proposed and a study focused on extreme risk is realised through an adapted backtesting. The second approach studied in this thesis is grounded on disappointment theory and implements a framework to calibrate disappointment risk premia to market prices. Based on a recent new axiomatisation, we show the mathematical properties of this risk premium and then develop a odel for the valuation of credit-default-swap in a mean-variance framework. We express closed-form formulae under two different assumptions for the recovery rate process. Finally we apply our model to series of market spreads and propose an algorithm for the calibration of each component of the risk premium, based on the minimisation of the square error. This leads us to the estimation of an optimal risk aversion parameter, an implied recovery rate and an implied recovery volatility. Performance of the algorithm is verified through comparison of the default probabilities issued from the model with risk-neutral and historical ones.
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