Importance Sampling Techniques for the Multidimensional Ruin Problem for General Markov Additive Sequences of Random Vectors

@inproceedings{Collamore2002ImportanceST,
  title={Importance Sampling Techniques for the Multidimensional Ruin Problem for General Markov Additive Sequences of Random Vectors},
  author={Jeffrey F. Collamore},
  year={2002}
}
Let {(Xn, Sn) : n = 0, 1, . . .} be a Markov additive process, where {Xn} is a Markov chain on a general state space and Sn is an additive component on R . We consider P {Sn ∈ A/ , some n} as → 0, where A ⊂ R is open and the mean drift of {Sn} is away from A. Our main objective is to study the simulation of P {Sn ∈ A/ , some n} using the Monte Carlo technique of importance sampling. If the set A is convex, then we establish: (i) the precise dependence (as → 0) of the estimator variance on the… CONTINUE READING

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