Single-index importance sampling with stratification. (English) Zbl 1524.62036
Summary: In many stochastic problems, the output of interest depends on an input random vector mainly through a single random variable (or index) via an appropriate univariate transformation of the input. We exploit this feature by proposing an importance sampling method that makes rare events more likely by changing the distribution of the chosen index. Further variance reduction is guaranteed by combining this single-index importance sampling approach with stratified sampling. The dimension-reduction effect of single-index importance sampling also enhances the effectiveness of quasi-Monte Carlo methods. The proposed method applies to a wide range of financial or risk management problems. We demonstrate its efficiency for estimating large loss probabilities of a credit portfolio under a normal and \(t\)-copula model and show that our method outperforms the current standard for these problems.
MSC:
| 62D05 | Sampling theory, sample surveys |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 65C05 | Monte Carlo methods |
| 91G10 | Portfolio theory |
Keywords:
single-index model; importance sampling; stratified sampling; quasi-Monte Carlo; loss probabilitiesReferences:
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