Abstract The most commonly used regression model in general insurance pricing is the compound Poisson with gamma claim sizes. There are two different parametrizations for this model: Poisson-gamma parametrization and Tweedie’s parametrization. Insurance industry typically prefers We review both parametrizations, provide new results that help to lower computational costs parameter estimation wit...

We consider compound geometric approximation for a nonnegative, integervalued random variable W . The bound we give is straightforward but relies on having a lower bound on the failure rate of W . Applications are presented to M/G/1 queuing systems, for which we state explicit bounds in approximations for the number of customers in the system and the number of customers served during a busy per...

This paper addresses the inventory penalty pricing problem under risk-neutral valuation principle. In particular, we consider an inventory driven by a constant replenishment rate and compound renewal demand stream (iid demand inter-arrival time and iid demand quantity), and subject to overage penalties and underage penalties. Our solution approach treats the inventory penalties of overage and u...

In this paper we compare ruin functions for two risk processes with respect to stochastic ordering, stop-loss ordering and ordering of adjustment coeecients. The risk processes are as follows: in the Markov-modulated environment and the associated averaged compound Poisson model. In the latter case the arrival rate is obtained by averaging over time the arrival rate in the Markov modulated mode...

In this article we consider the Levy processes and the corresponding semi-group. We represent the generator of this semigroup in a convolution form. Using the obtained convolution form and the theory of integral equations we investigate the properties of a wide class of Levy processes (potential, quasi-potential, the probability of the Levy process remaining within the given domain, long time b...