Importance sampling techniques for the multidimensional ruin problem for general Markov additive sequences of random vectors
Let \(\{S_n\}\) be a sequence of \(\mathbb{R}^n\)-valued random variables and let \(A\subset\mathbb{R}^n\) be open. Consider the hitting probability of a region \(A/\varepsilon: \{x/\varepsilon: x\in A\}\), by \(\{S_n\}\) as \(\varepsilon\to 0\). It is assumed that the mean drift of \(\{S_n\}\) is directed away from \(A\) so that this probability tends to zero as \(\varepsilon\to 0\). The aim of this paper is to use importance sampling for simulating it. For any fixed \(\varepsilon\), an efficient estimate is obtained which has certain optimality properties as \(\varepsilon\to 0\).
scientific article; zbMATH DE number 1906197
scientific article