Efficient importance sampling in ruin problems for Multidimensional Regularly Varying Random Walks (with J. C. Liu)

Summary:

This paper focuses on a multidimensional version of Blanchet and Glynn (2008) Ann. of Appl. Probab. 18, 1351-1378, under regularly varying assumptions. Questions on large deviations for multidimensional heavy-tailed random walks are very challenging. In fact, the definition of multivariate regular variation is not powerful enough to describe how rare events happen in this setting, unless the rare events can be shown to occur because of a single large jump. This paper concentrates on this particular scenario and provides strongly efficient estimators based on Lyapunov bounds.

Bibtex:

@Article{BlaLiu2010,

author = { J. Blanchet and J. C. Liu},

title = {Efficient importance sampling in ruin problems for multidimensional regularly varying random walks},

journal = {Journal of Applied Probability},

year = {2010},

volume = {47},

pages = {301-322}

}