Efficient Rare Event Simulation of Continuous Time Markovian Perpetuities (with P. Glynn)

Summary:

We develop an asymptotically optimal rare event simulation estimator for the tail of a perpetuity of the form

D=∫_[₀_,∞)exp(-α∫_[₀_,t]γ(X(s))ds)λ(X(t))dt,

where X(.) is a continuous time Markov chain. The function γ(.) can be interpreted as the interest rate and λ(.) as the discount rate. The parameter α scales the interest rates and we show the optimality of the algorithm as α goes to zero and looking at tails of D at levels c/α assuming that c is large enough. That is, we look at rare event simulation in the setting of low interest rates. The importance sampler is state-dependent and it actually depends, at time t, on the value of X(t) and on the value of ∫_[₀_,t]γ(X(s))ds . I like the paper because it is easy to read and has a couple of nice tricks on rare-event simulation and changes-of-measure that is good to keep in mind. I sometimes assign this paper to students because it allows them to get familiar with these types of techniques.

Bibtex:

@INPROCEEDINGS {BlaGlynWSCCTP09,

AUTHOR={J. Blanchet and P. Glynn },

YEAR={2009},

TITLE={Efficient rare event simulation of continuous time Markovian perpetuities},

BOOKTITLE={Proceedings of the 2009 Winter Simulation Conference},

EDITOR={M. D. Rossetti, R. R. Hill, B. Johansson, A. Dunkin, and R. G. Ingalls},

PUBLISHER={IEEE Press},

PAGES={444-451}

}