A unified approach for finite-dimensional, rare-event Monte Carlo simulation

We consider the problem of estimating the small probability that a function of a finite number of random variables exceeds a large threshold. Each input random variable may be light-tailed or heavy-tailed. Such problems arise in financial engineering and other areas of operations research. Specific problems in this class have been considered earlier in the literature, using different methods that depend on the special properties of the particular problem. Using the Laplace principle (in a restricted finite-dimensional setting), this paper presents a unified approach for deriving the log-asymptotics, and developing provably efficient fast simulation techniques using the importance sampling framework of hazard rate twisting.