Efficient simulation of finite horizon problems in queueing and insurance risk
by Leonardo Rojas-Nandayapa and Søren Asmussen
Research Reports
Number 490 (March 2007)
Let $\psi(u,t)$ be the probability that the workload in an initially empty M/G/1 queue exceeds $u$ at time $t<\infty$, or, equivalently, the ruin probability in the classical Crámer-Lundberg model. Assuming service times/claim sizes to be subexponential, various Monte Carlo estimators for $\psi(u,t)$ are suggested. A key idea behind the estimators is conditional Monte Carlo. Variance estimates are derived in the regularly varying case, the efficiencies are compared numerically and also one of the estimators is shown to have bounded relative error. In part, also extensions to general Léevy processes are treated.
This primarily serves as Thiele Research Reports number 3-2007, but was also published in Research Reports