Modeling the interactions between a reinsurer and several insurers, or between a central management branch (CB) and several subsidiary business branches, or between a coalition and its members, are fascinating problems, which suggest many interesting questions. Beyond two dimensions, one cannot...

As is well-known, the benefit of restricting Lévy processes without positive jumps is the ' W,Z scale functions paradigm', by which the knowledge of the scale functions W,Z extends immediately to other risk control problems. The same is true largely for strong Markov processes X t , with the...

The Segerdahl-Tichy Process, characterized by exponential claims and state dependent drift, has drawn a considerable amount of interest, due to its economic interest (it is the simplest risk process which takes into account the effect of interest rates). It is also the simplest non-Lévy,...

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...

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...

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)&#x2212;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>