ﻻ يوجد ملخص باللغة العربية
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 the ruin probability in this situation. The resulting estimators perform well for both small and large initial capital. We quantify the variance reduction as well as the efficiency gain of our method over another fast standard technique based on the classical Pollaczek-Khinchine formula. We provide a numerical example to illustrate the performance, and show that for more time-consuming conditional Monte Carlo techniques, the new series representation also does not compare unfavorably to the one based on the Pollaczek- Khinchine formula.
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
We investigate the probability that an insurance portfolio gets ruined within a finite time period under the assumption that the r largest claims are (partly) reinsured. We show that for regularly varying claim sizes the probability of ruin after rei
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
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
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