In a bonus-malus system in car insurance, the bonus class of a customer is updated from one year to the next as a function of the current class and the number of claims in the year (assumed Poisson). Thus the sequence of classes of a customer in consecutive years forms a Markov chain, and most...

Phase-type (PH) distributions are defined as distributions of lifetimes of finite continuous-time Markov processes. Their traditional applications are in queueing, insurance risk, and reliability, but more recently, also in finance and, though to a lesser extent, to life and health insurance....

Two insurance companies I 1 ,I 2 with reserves R 1 (t),R 2 (t) compete for customers, such that in a suitable differential game the smaller company I 2 with R 2 (0)<R 1 (0) aims at minimizing R 1 (t)−R 2 (t) by using the premium p 2 as control and the larger I 1 at maximizing by using p 1. Deductibles K 1 ,K 2 are fixed but may be different. If K 1 >K 2 and I 2 is the leader choosing its premium first, conditions for Stackelberg equilibrium are established. For gamma-distributed...</r>

Well-behaved densities are typically log-convex with heavy tails and log-concave with light ones. We discuss a benchmark for distinguishing between the two cases, based on the observation that large values of a sum X1+X2 occur as result of a single big jump with heavy tails whereas X1,X2 are of...