Parisian ruin of self-similar Gaussian risk processes
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In this paper, the authors derived the exact asymptotics of the probability of Parisian ruin for self-similar Gaussian risk processes and derived the normal approximation of the Parisian time.Abstract:
In this paper we derive the exact asymptotics of the probability of Parisian ruin for self-similar Gaussian risk processes. Additionally, we obtain the normal approximation of the Parisian ruin time and derive an asymptotic relation between the Parisian and the classical ruin times.read more
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Extremes of vector-valued Gaussian processes: exact asymptotics
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Extremes of vector-valued Gaussian processes: exact asymptotics
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Uniform tail approximation of homogenous functionals of Gaussian fields
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Extremal behavior of hitting a cone by correlated Brownian motion with drift
TL;DR: In this paper, the authors derived exact asymptotic expression for P x u { ∃ t ≥ 0 X (t ) − μ t ∈ U }, as u → ∞, where X ( t ) = ( X 1 ( t ), …, X d ( t )) ⊤, t ≥0 is a correlated d-dimensional Brownian motion starting at the point x u = − α u with α ∈ R d, μ ∈R d and U = ∏ i = 1 d [ 0, ∞ ).
References
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Book
Asymptotic Methods in the Theory of Gaussian Processes and Fields
TL;DR: In this article, the double sum method and the method of moments limit theorems for the number of high excursions and for maxima of Gaussian processes and fields are studied.
Book
Sojourns and Extremes of Stochastic Processes
TL;DR: A survey of the normal distribution can be found in this paper, where the authors consider the following classes of Gaussian processes: (1) Stationary Gaussian Processes on a finite interval (2) Processes with stationary independent increments.
Journal ArticleDOI
Brownian excursions and parisian barrier options
TL;DR: In this article, the authors study a new variant of the so-called barrier option: a down-and-out barrier option becomes worthless as soon as a barrier is reached, whereas a down and-out Parisian barrier option is lost by the owner if the underlying asset reaches a prespecified level and remains constantly below this level for a time interval longer than a fixed number.