Efficient Rare-event Simulation for Perpetuities

Details Efficient Rare-event Simulation for Perpetuities Efficient Rare-event Simulation for Perpetuities

2012-01-17

arxiv.org/abs/1201.3419v1

Mathematics

Probability

Scientific paper

We consider perpetuities of the form D = B_1 exp(Y_1) + B_2 exp(Y_1+Y_2) + ... where the Y_j's and B_j's might be i.i.d. or jointly driven by a suitable Markov chain. We assume that the Y_j's satisfy the so-called Cramer condition with associated root theta_{ast} in (0,infty) and that the tails of the B_j's are appropriately behaved so that D is regularly varying with index theta_{ast}. We illustrate by means of an example that the natural state-independent importance sampling estimator obtained by exponentially tilting the Y_j's according to theta_{ast} fails to provide an efficient estimator (in the sense of appropriately controlling the relative mean squared error as the tail probability of interest gets smaller). Then, we construct estimators based on state-dependent importance sampling that are rigorously shown to be efficient.

Affiliated with

Also associated with

No associations

Rating

Efficient Rare-event Simulation for Perpetuities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Efficient Rare-event Simulation for Perpetuities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Efficient Rare-event Simulation for Perpetuities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-96645