A two-dimensional ruin problem on the positive quadrant

A two-dimensional ruin problem on the positive quadrant

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 ...

A Two-dimensional Ruin Problem on the Positive Quadrant, with Exponential Claims: Feynman-kac Formula, Laplace Transform and Its Inversion

We consider an exit problem of a certain two-dimensional process from a cone, inspired by applications in insurance and queueing theory. One motivation is to study the joint ruin problem for two insurance companies (insurance/reinsurance), or for two branches of the same company, which divide between them both claims and premia in some specified proportions, the goal being to split the risk (in...

On a Generalized Ruin Problem

Exit problem of a two - dimensional risk process from the quadrant : exact and asymptotic results

Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem considered is that of the corresponding two-dimensional risk process first leaving the positive quadrant; another is that of entering the negative quadrant. When th...

ar X iv : 0 71 1 . 24 65 v 1 [ m at h . PR ] 1 5 N ov 2 00 7 A two - dimensional ruin problem on the positive quadrant

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 ...