In this paper, a particular class of matrix-exponential distributions is described, also with respect to its use in risk theory, namely phase-type distributions. Phase-type distributions have the important advantage of being suitable for approximating most of other distributions as well as being mathematically tractable. After a review on phase-type distributions and their properties, it is illustrated a possible use in risk theory. Modelling both interarrival claim times and individual claim sizes with this class of distributions an explicit formula for the probability of ultimate ruin is given.
Carleo, A., Pietroluongo, M. (2008). On matrix-exponential distributions in Risk Theory. In Proceedings of X Italian-Spanish Congress of Financial and Actuarial Mathematics.
On matrix-exponential distributions in Risk Theory
CARLEO, Alessandra;
2008-01-01
Abstract
In this paper, a particular class of matrix-exponential distributions is described, also with respect to its use in risk theory, namely phase-type distributions. Phase-type distributions have the important advantage of being suitable for approximating most of other distributions as well as being mathematically tractable. After a review on phase-type distributions and their properties, it is illustrated a possible use in risk theory. Modelling both interarrival claim times and individual claim sizes with this class of distributions an explicit formula for the probability of ultimate ruin is given.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
