Learn More
In this paper we clarify dependence properties of elliptical distributions by deriving general but explicit formulas for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regularly varying if and only if the bivariate marginal distributions(More)
We study the extremal behavior of a stochastic integral driven by a multivariate Lévy process that is regularly varying with index α > 0. For predictable integrands with a finite (α + δ)-moment, for some δ > 0, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving Lévy process and we determine its limit measure(More)
Dedicated to the memory of Alexander V. Nagaev We extend classical results by A. on large deviations for sums of i.i.d. regularly varying random variables to partial sum processes of i.i.d. regularly varying vectors. The results are stated in terms of a heavy-tailed large deviation principle on the space of c`adì ag functions. We illustrate how these(More)
A random vector X with representation X = j≥0 AjZj is considered. Here, (Zj) is a sequence of independent and identically distributed random vectors and (Aj) is a sequence of random matrices, 'predictable' with respect to the sequence (Zj). The distribution of Z1 is assumed to be multivariate regular varying. Moment conditions on the matrices (Aj) are(More)
Computation of extreme quantiles and tail-based risk measures using standard Monte Carlo simulation can be inefficient. A method to speed up computations is provided by importance sampling. We show that importance sampling algorithms, designed for efficient tail probability estimation, can significantly improve Monte Carlo estimators of tail-based risk(More)
Within-die process variations arise during integrated circuit (IC) fabrication in the sub-100nm regime. These variations are of paramount concern as they deviate the performance of ICs from their designers' original intent. These deviations reduce the parametric yield and revenues from integrated circuit fabrication. In this paper we provide a complete(More)
In some recent papers (Elliott and van der Hoek, 2003; Hu and Øksendal, 2003) a fractional Black-Scholes model have been proposed as an improvement of the classical Black-Scholes model (see also Benth, 2003; Biagini et al., 2002; Biagini and Øksendal, 2004). Common to these fractional Black-Scholes models, is that the driving Brownian motion is replaced by(More)
In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve according to quite general semimartingales. We show that the ruin problem corresponds to determining hitting probabilities for(More)
State-dependent importance sampling algorithms based on mixtures are considered. The algorithms are designed to compute tail probabilities of a heavy-tailed random walk. The increments of the random walk are assumed to have a regularly varying distribution. Sufficient conditions for obtaining bounded relative error are presented for rather general mixture(More)