Efficient Simulation and Conditional Functional Limit Theorems for Ruinous Heavy-tailed Random Walks (with J. C. Liu).

Summary:

This is a follow up work on an algorithm by Blanchet and Glynn (2008) Ann. of Appl. Probab. 18, 1351-1378 for the estimation of the ruin probability under a heavy-tailed random walk model. A problem with such algorithm is the evaluation of certain normalizing constants. This is not challenging in one dimension but the prospect of extending the theory to higher dimensions calls for overcoming this problem. The present paper deals with this issue in a very convenient way by proposing a suitable mixture family of samplers. We make a case for the whole approach, which combines the family of samplers with Lyapunov bounds, not only as a simulation methodology but as a technique to develop asymptotics. We prove conditional functional CLTs given ruin and strong optimality results for simulation. For instance, we argue that one can obtain strongly efficient estimators with linear complexity basically if and only if the increments have at least 3/2 moments.

Bibtex:

@Article{BlanLiu_TVW10,

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

title = {Efficient Simulation and Conditional Functional Limit Theorems for Ruinous Heavy-tailed Random Walks},

journal = {Preprint},

year = {2010},

volume = {},

pages = {}

}