We study the shape of the log-returns density $f(x)$ in a CGMY L\'evy process $X$ with given skewness $S$ and kurtosis $K$ of $X(1)$ and without a Brownian component. The jump part of such a process is specified by the L\'evy density which is $C\e^{-Mx}/x^{1+Y}$ for $x0$ and...

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...

Algorithms for simulation of a Lévy process X(t) are discussed, with particular emphasis on two algorithms approximating jumps that are in some sense small. One is classical, defining small jumps as those of small absolute value. The other one appears to be new and relies on an completely...

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....