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pro vyhledávání: '"Jasnovidov, Grigori"'
Autor:
Jasnovidov, Grigori
In this contribution we study the asymptotics of \begin{eqnarray*} P(\exists t\ge 0 : B_H(L(t))-cL(t)>u), \quad u \to \infty, \end{eqnarray*} where $B_H, H\in (0,1)$ is a fractional Brownian motion, $L(t)$ is a non-negative pure jumps L\'{e}vy proces
Externí odkaz:
http://arxiv.org/abs/2312.09389
In this paper we derive an upper bound for the difference between the continuous and discrete Piterbarg constants. Our result allows us to approximate the classical Piterbarg constants by their discrete counterparts using Monte Carlo simulations with
Externí odkaz:
http://arxiv.org/abs/2209.13972
For $\{X(t), t \in G_\delta\}$ a centered Gaussian process with stationary increments and a.s. sample paths on a discrete grid $G_\delta=\{0,\delta,2\delta, ...\}$, where $\delta>0$, we investigate the stationary reflected process $$Q_{\delta,X}(t) =
Externí odkaz:
http://arxiv.org/abs/2206.14712
In this manuscript, we address open questions raised by Dieker \& Yakir (2014), who proposed a novel method of estimation of (discrete) Pickands constants $\mathcal{H}^\delta_\alpha$ using a family of estimators $\xi^\delta_\alpha(T), T>0$, where $\a
Externí odkaz:
http://arxiv.org/abs/2108.00756
Autor:
Jasnovidov, Grigori
This paper derives the asymptotic behavior of $$\mathbb{P} \{ \int\limits_0^\infty \mathbb{I}\Big(B_H(s)-c_1s>q_1u, B_H(s)-c_2s>q_2u\Big)ds>T_u\},\quad u \to \infty,$$ where $B_H$ is a fractional Brownian motion, $c_1,c_2,q_1,q_2>0,\ H \in (0,1), \ T
Externí odkaz:
http://arxiv.org/abs/2107.11322
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 April 2024 532(1)
In this contribution we study asymptotics of the simultaneous Parisian ruin probability of a two-dimensional fractional Brownian motion risk process. This risk process models the surplus processes of an insurance and a reinsurance companies, where th
Externí odkaz:
http://arxiv.org/abs/2103.03213
Autor:
Jasnovidov, Grigori
This paper derives the asymptotic behavior of the following ruin probability $$P\{\exists t \in G(\delta):B_H(t)-c_1t>q_1u,B_H(t)-c_2t>q_2u\}, \ \ \ u \rightarrow \infty,$$ where $B_H$ is a standard fractional Brownian motion, $c_1,q_1,c_2,q_2>0$ and
Externí odkaz:
http://arxiv.org/abs/2002.04928
Autor:
Jasnovidov, Grigori
We analyze the classical Brownian risk models discussing the approximation of ruin probabilities (classical, {\gamma}-reflected, Parisian and cumulative Parisian) for the case that ruin can occur only on specific discrete grids. A practical and natur
Externí odkaz:
http://arxiv.org/abs/2001.10311
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