Efficient simulation of finite horizon problems in queueing and insurance risk

摘要

Let ψ{u,t) be the probability that the workload in an initially empty M/G/1 queue exceeds u at time t < ∞, or, equivalently, the ruin probability in the classical Cramer-Lundberg model. Assuming service times/claim sizes to be subexponential, various Monte Carlo estimators for ψ{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 the estimators are shown to have bounded relative error in some main cases. In part, also extensions to general Levy processes are treated.