Recently, Albrecher and his coauthors have published a series of papers on the ruin probability of the Lévy insurance model under the so-called loss-carry-forward taxation, meaning that taxes are paid at a certain …xed rate immediately when the surplus of the company is at a running maximum. In this paper we assume periodic taxation under which the company pays tax at a …xed rate on its net inc...

We study a new technique for the asymptotic analysis of heavy-tailed systems conditioned on large deviations events. We illustrate our approach in the context of ruin events of multidimensional regularly varying random walks. Our approach is to study the Markov process described by the random walk conditioned on hitting a rare target set. We construct a Markov chain whose transition kernel can ...

This paper investigates the moments of the surplus before ruin and the deficit at ruin in the Erlang(2) risk process. Using the integro-differential equation that we establish, we obtain some explicit expressions for the moments. Furthermore, when the claim size is exponentially and subexponentially distributed, asymptotic relationships for the moments are derived as the initial capital tends t...

In this paper we want to investigate the following problem: For a given upper bound for the ruin probability, maximize the expected discounted consumption of an investor in finite time. The endowment of the agent is modeled by Brownian motion with positive drift. We give an iterative algorithm for the solution of the problem, where in each step an unconstraint, but penalized, problem is solved....

Based on Invariance Principle for Brownian Motion, we obtained a closed-form expression of the ruin probability Discrete-Time Risk Model with Random Premiums that was recently introduced by Korzeniowski [1]. We show in this model, given two strategies have same ultimate ruin, strategy larger initial capital and smaller loading factor is less risky than it lowers finite time horizon.