Abstract

Probability distortion has been a means of pricing in insurance and finance for a long time. It is often utilized to transform the loss probability distribution to another distribution that assigns more weight to the outstanding potential losses. Parametric models for multivariate distributions can be proposed based on the extension of distortion transformations to the multivariate framework, which allows for generating new families of copulas from an existing one. These parametric representations are used in order to relate the distribution of bivariate climate extreme realizations to the distribution of projected extremes in the long term. The focus of this thesis is on modeling the bivariate distribution of temperature and precipitation annual maxima in Montreal by Extreme Value Theory, and propose a distortion of this model to explain the future projections based on three emissions scenarios representing different atmospheric concentrations of greenhouse gases (RCP 2.6, RCP 4.5 and RCP 8.5). Lastly, Akaike information criterion (AIC) and Bayesian information criterion (BIC) are employed to compare the performance of different distortions.