We study the distribution of the stochastic integral [integral operator]0t8e-Rt dPt where R is a Brownian motion with positive drift and P is an independent compound Poisson process. We show that in the special case when the jumps of P are exponentially distributed, the integral has the same...

We introduce a general model to describe the risk process of an insurance company. This model allows for stochastic rate of return on investments as well as stochastic level of inflation, thus in theory enabling a decision maker to choose between insurance and investment risk. In the first part...

We study the distribution of the stochastic integral [integral operator][infinity]0e-RtdPt where P and R are independent Lévy processes with a finite number of jumps on finite time intervals. The exact distribution is obtained in many special cases, and we derive asymptotic properties of the...

We consider a classical risk process compounded by another independent process. Both of these component processes are assumed to be Lévy processes. Sharp conditions are given on the parameters of these two components to ensure when ruin is certain, and also when the time of ruin is of...

In Bai and Paulsen [L. Bai, J. Paulsen, Optimal dividend policies with transaction costs for a class of diffusion processes, SIAM J. Control Optim. 48 (2010) 4987–5008] the optimal dividend problem under transaction costs was analyzed for a rather general class of diffusion processes. It was...