Large Deviations and Importance Sampling

Specialeforsvar ved Camilla Nicole Schaldemose

Titel:  Large Deviations and Importance Sampling

Abstract: The goal of the thesis is to connect large deviation methods to the development of efficient importance sampling schemes. The thesis will show that efficient importance sampling algorithms can be obtained when applying the change of measure suggested by a large deviation analysis. Furthermore, it is shown that a collection of efficient importance sampling algorithms can be found through a minimization procedure, namely by minimizing the rate function in Mogulskii's Theorem. Counterexamples of this efficiency, as studied by Glasserman (1996), are considered, and A theorem characterizing the decay rate of the second moment of a general importance sampling estimator is proved. As a possible alternative to the standard importance sampling scheme, the thesis studies contemporary state-dependent methods based on subsolutions to an Isaacs equation as introduced in the recent work of Dupuis and Wang (2004, 2007). The thesis will compare these state-dependent schemes to more classical importance sampling schemes in various numerical examples such as the multidimensional ruin problem. 

Vejleder:    Jeffrey Collamore
Censor:     Søren Asmussen, Aarhus Universitet