Αρχές υπολογισμού ασφαλίστρου και μέτρα κινδύνου στην αναλογιστική επιστήμη
Principles of premium calculation and risk measures in actuarial science
One of the most important problems encountered in actuarial science is the determination of the premium for a loss portfolio, with at least partial knowledge of the magnitude of these losses. For the calculation of the annual premium in such a portfolio, alternative principles may be used, such as the principle of variance, the principle of standard deviation, the exponential principle, etc. Also, in order to determine the premium in such a way that the portfolio is both competitive and highly solvent (ie low probability of ruin), various risk measures have been proposed, the most popular of which is Value at Risk. This dissertation will give an overview of the main principles of premium calculation and examine to what extent they meet different desirable attributes (eg consistency, additivity, repeatability, etc.). In addition, the main risk measures used in actuarial science (VaR, TVaR, Expected Shortfall) will be presented. Finally, the risk measures will be compared for specific theoretical distributions with heavy tail.