Grant: Discovery Grants Program - Individual

Risk management is of prime importance in financial institutions engaged in financial uncertainties, and risk measurement is its natural precursor. In light of this, at least three substantial subjects have to be addressed: the multivariate probabilistic model possessing a convenient dependence structure - to describe risks' behavior; the choice of appropriate risk functionals - to translate the implications of the model to risk parlance; and the (analytical) solutions for the latter in the framework of the former - to, actually, measure risk. The present project is intended to contribute to the aforementioned pillars of 'successful' risk measurement. Namely, we shall first propose and investigate a number of new multivariate probabilistic models having convenient dependence structures and important, especially in finance and actuarial science, univariate marginal distributions. Briefly, the herein suggested models can be considered multivariate generalizations of the well known univariate exponential dispersion models. In this project, the multivariate densities of the aforementioned multivariate classes of distributions, their higher order (conditional) moments and products of these moments, Chebyshev's type inequalities, asymptotic behaviors and second order optimal estimation techniques will be developed. In addition, we shall accomplish a thorough risk analysis in the framework of the suggested models. Applying some powerful tail-based risk functionals e.g. the tail conditional expectation and the tail variance premiums, we shall obtain analytical expressions for 1.) the risk of the whole financial institution (risk inherent in the convolution of the univariate dependent marginals), and 2.) the consequent allocation of this risk to its sources (risk contribution of each marginal to the measure obtained in Point 1 bearing in mind the existing dependence structure). Numerous simulation studies and a software packet will be produced to illustrate the results.