arXiv subjects

Mathieu Cambou

Publications and source records attributed to Mathieu Cambou.

2 recordsLinked to original sources

arXiv2015

Quasi-random numbers for copula models

The present work addresses the question how sampling algorithms for commonly applied copula models can be adapted to account for quasi-random numbers. Besides sampling methods such as the conditional distribution method (based on a one-to-one transformation), it is also shown that typically faster sampling methods (based on stochastic representations) can be used to improve upon classical Monte Carlo methods when pseudo-random number generators are replaced by quasi-random number generators. This opens the door to quasi-random numbers for models well beyond independent margins or the multivariate normal distribution. Detailed examples (in the context of finance and insurance), illustrations and simulations are given and software has been developed and provided in the R packages copula and qrng.

stat.CO↗

arXiv2014

An importance sampling approach for copula models in insurance

An importance sampling approach for sampling copula models is introduced. We propose two algorithms that improve Monte Carlo estimators when the functional of interest depends mainly on the behaviour of the underlying random vector when at least one of the components is large. Such problems often arise from dependence models in finance and insurance. The importance sampling framework we propose is general and can be easily implemented for all classes of copula models from which sampling is feasible. We show how the proposal distribution of the two algorithms can be optimized to reduce the sampling error. In a case study inspired by a typical multivariate insurance application, we obtain variance reduction factors between 10 and 30 in comparison to standard Monte Carlo estimators.

stat.CO↗