- Numerical Techniques in Lévy Fluctuation Theory
- Methodology and Computing in Applied Probability
- Volume | Issue number
- 16 | 1
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
This paper presents a framework for numerical computations in fluctuation theory for Lévy processes. More specifically, with X¯t:=sup0≤s≤tXs denoting the running maximum of the Lévy process X t , the aim is to evaluate P(X¯t≤x) for t,x > 0. We do so by approximating the Lévy process under consideration by another Lévy process for which the double transform Ee−αX¯τ(q) is known, with τ(q) an exponentially distributed random variable with mean 1/q; then we use a fast and highly accurate Laplace inversion technique (of almost machine precision) to obtain the distribution of X¯t . A broad range of examples illustrates the attractive features of our approach.
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