Θεωρία πληροφορίας, μέτρα αβεβαιότητας εντροπίας και εφαρμογές στον αναλογισμό
Τιπαπίδη - Καραμαϊλή, Αλεξάνδρα
The main objective of the field of Actuarial Science is the analysis and valuation of economic consequences that refer to risks and uncertain future events. The necessity to quantify the uncertainty conditions of an event has led to the use of measures of entropy and uncertainty. In the following thesis, various measures of entropy are to be analyzed, and their applications in Actuarial Science are to be examined. Specifically, the first chapter contains a summary of the history of Information Theory and its extension in Actuarial Science. After that, in the second chapter we will define Shannon’s Entropy and some features of this measure. We will also examine its application in Loss Models, under the influence of inflation. In the third chapter, the Kullback-Leibler Divergence is defined, and the application of the Minimum Discrimination Information linear problem in the assumption of Uniform Distribution of Deaths (UDD) and Constant Force of Mortality is described. The fourth and fifth chapter of this thesis explore the measures of Residual and Past Entropy respectively, and also their application in truncated or censored loss data, as well as in Survival Models. Finally, in the sixth chapter we will examine the measures of Cumulative Entropies; Cumulative Residual Entropy, Dynamic Cumulative Residual and Doubly Truncated Cumulative Residual Entropy, in relation to their properties, and the categorization of distributions in aging classes.