Uncertainty measures and actuarial application

Abstract

<p>Predmet istraživanja ovog rada su mere neodređenosti, posebno mera<br />kredibliteta, kao i mogućnost njihove primene u aktuarstvu. U cilju<br />generalizacije teorije kredibiliteta, uvedena je nova mera, nazvana mera c-<br />kredibiliteta. Mera c-kredibiliteta na X je skupovna funkcija takva da su<br />zadovoljene osobine normalnosti, monotonosti, samodualnosti i maksimalnosti.<br />Za nju su dokazane neke osobine kao što su npr. subaditivnost i<br />poluneprekidnost. Nadalje, definisan je integral zasnovan na meri c-<br />kredibiliteta, a navedena su i dokazana određena svojstva. Nova mera je uvedena<br />i u fazi okruženju kao agregirana vrednost mera mogućnosti i neophodnosti.</p>

<p>This thesis studies uncertainty measures, especially credibility measure, as well as<br />the possibility of their application in actuaries. In order to generalize credibility theory,<br />a new fuzzy measure is proposed, called c &minus; credibility measure. C &minus; credibility<br />measure on X is a set function that satisfies normality, monotonicity, self-duality and<br />maximality. Certain properties of the c&minus;credibility measure are proved, such as, for<br />example, subadditivity and semicontinuity. Furthermore, an integral based on this<br />measure is defined, in analogy to the existing integrals, and its properties are proved.<br />Then, the credibility measure in a fuzzy environment is introduced as the aggregate<br />value of the possibility and necessity measures.</p>