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...

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...