This paper considers the distribution of some extremum on the risk process whose income depend on the current reserve. We first construct the defective renewal sequence and obtain the density function of them. By the presented renewal measure and the strong Markov property, the distribution of the first hitting time is obtained explicitly. Then, the ruin probability and the probability that the...

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance companies by Cramér-Lundberg processes we obtain the Laplace transform in space of the probability that ...

We consider a compound Poisson risk model where part of the premium is paid to the shareholders as dividends when the surplus exceeds a specified threshold level. In this model, we are interested in computing the moments of the total discounted dividends paid until ruin occurs. However, instead of employing the traditional argument which involves conditioning on the time and amount of the first...

The purpose of this paper is to explore a discrete-time cash flow optimization problem the insurance company with time value ruin under different interest rates. For sake considering ruin, we assume that shareholders can get subsidies per unit time, as long not bankrupt. switching rates on market controlled by stationary Markov chain. dynamic programming principle used solve problem. By using m...

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...

Properties of the distribution of the deficit at ruin in the stationary renewal risk model are studied. A mixture representation for the conditional distribution of the deficit at ruin (given that ruin occurs) is derived, as well as a stochastic decomposition involving the residual lifetime associated with the maximal aggregate loss. In the case where the individual claims have a phase-type dis...

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...