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The classical Cramer-Lundberg risk process models the ruin probability of an insurance company experiencing an incoming cash flow - the premium income, and an outgoing cash flow - the claims. From a systems viewpoint, the web of insurance agents and risk objects can be represented by a bipartite network. In such a bipartite network setting, it has been shown that joint ruin of a group of agents may be avoided even if individual agents would experience ruin in the classical Cramer-Lundberg model. This paper describes and examines a phase transition phenomenon for these ruin probabilities.
In this paper we give few expressions and asymptotics of ruin probabilities for a Markov modulated risk process for various regimes of a time horizon, initial reserves and a claim size distribution. We also consider f
This paper develops asymptotics and approximations for ruin probabilities in a multivariate risk setting. We consider a model in which the individual reserve processes are driven by a common Markovian environmental process. We subsequently consider a
Our work aims to study the tail behaviour of weighted sums of the form $sum_{i=1}^{infty} X_{i} prod_{j=1}^{i}Y_{j}$, where $(X_{i}, Y_{i})$ are independent and identically distributed, with common joint distribution bivariate Sarmanov. Such quantiti
The study deals with the ruin problem when an insurance company having two business branches, life insurance and non-life insurance, invests its reserve into a risky asset with the price dynamics given by a geometric Brownian motion. We prove a resul
We consider the classical Cramer-Lundberg risk model with claim sizes that are mixtures of phase-type and subexponential variables. Exploiting a specific geometric compound representation, we propose control variate techniques to efficiently simulate