We consider an M/G/1 retrial queue, where the service time distribution has a regularly varying tail with index −β, 1 < β < 2. It is shown that the waiting time distribution has a regularly varying tail with index 1− β, and the pre-factor is determined explicitly. The result is obtained by comparing the waiting time in the M/G/1 retrial queue with the waiting time in the ordinary M/G/1 queue wi...

In this paper we study the distributional tail behavior of the solution to a linear stochastic differential equation driven by infinite variance α-stable Lévy motion. We show that the solution is regularly varying with index α. An important step in the proof is the study of a Poisson number of products of independent random variables with regularly varying tail. The study of these products dese...

We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. We prove that the model eventually localises on exactly two sites with overwhelming probability. This is a stronger form of localisation than has previously been established in the literature for the Bouchaud trap model on the integers in the case of regularly varyin...

Using copulas, in this paper we investigate the static and dynamic extreme dependence of international stock markets. We examine both the structure and the degree of the dependence. The data set are daily returns on the stock indices from countries in North America, Europe and East Asia. The results show signi…cant asymmetric tail dependence in most of the return pairs, with the overall lower t...

Tail risk refers to the risk associated with extreme values and is often affected by extremal dependence among multivariate extremes. Multivariate tail risk, as measured by a coherent risk measure of tail conditional expectation, is analyzed for multivariate regularly varying distributions. Asymptotic expressions for tail risk are established in terms of the intensity measure that characterizes...

Multivariate coherent risks can be described as classes of portfolios consisting of extra capital reserves that are used to cover potential losses under various scenarios. Tail risk refers to the risk associated with extremal events and is often affected by extremal dependence among multivariate extremes. Multivariate tail risk, as measured by a coherent risk measure of tail conditional expecta...

In this paper, we introduce a new time series model having stochastic exponential tail. This is constructed based on the Normal Tempered Stable distribution with time-varying parameter. The captures tail, which generates volatility smile effect and term structure in option pricing. Moreover, describes of volatility. We empirically show skewness kurtosis by applying to analyze S&P 500 index retu...

We characterize joint tails and tail dependence for a class of stochastic volatility processes. We derive the exact joint tail shape of multivariate stochastic volatility with innovations that have a regularly varying distribution tail. This is used to give four new characterizations of tail dependence. In three cases tail dependence is a non-trivial function of linear volatility memory paramet...

We characterize joint tails and tail dependence for a class of stochastic volatility processes. We derive the exact joint tail shape of multivariate stochastic volatility with innovations that have a regularly varying distribution tail. This is used to give four new characterizations of tail dependence. In three cases tail dependence is a non-trivial function of linear volatility memory paramet...