Modern Stochastics-Theory and Applications

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ISSN:: 2351-6054
Category:: STATISTICS & PROBABILITY
Impact factor:: 0.7

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Some continuity estimates for ruin probability and other ruin-related quantities

2026-03-25

Lazaros Kanellopoulos

In this paper we investigate continuity properties for ruin probability in the classical risk model. Properties of contractive integral operators are used to derive continuity estimates for the deficit at ruin. These results are also applied to obtain desired continuity inequalities in the setting of continuous time surplus process perturbed by diffusion. In this framework, the ruin probability can be expressed as the convolution of a compound geometric distribution K with a diffusion term. A continuity inequality for K is derived and an iterative approximation for this ruin-related quantity is proposed. The results are illustrated by numerical examples. PDF    XML

The generalization of several classical estimators for a positive extreme value index

2026-03-18

Marijus Vaičiulis

In this paper, we introduce a family of semi-parametric estimators for the positive extreme value index γ , parameterized in two tuning parameters. The asymptotic normality of the introduced estimators is proved. It is shown that the partial case of newly introduced estimators (a subfamily with one tuning parameter) has quite good asymptotic properties and dominates several previously introduced estimators. Small Monte-Carlo simulations are included. Also, the performance of this parameterized subfamily of estimators is illustrated for pair exchange ratio data sets. PDF    XML

Convergence of random walks in ℓp-spaces of growing dimension

2026-03-11

Bochen Jin

We prove a limit theorem for paths of random walks with n steps in ${\mathbb{R}^{d}}$ as n and d both go to infinity. For this, the paths are viewed as finite metric spaces equipped with the ${\ell _{p}}$ -metric for $p\in [1,\infty )$ . Under the assumptions that all components of each step are uncorrelated, centered, have finite $2p$ -th moments, and are identically distributed, we show that such random metric space converges in probability to a deterministic limit space with respect to the Gromov-Hausdorff distance. This result generalises earlier work by Kabluchko and Marynych [Ann. Inst. H. Poincaré Probab. Statist. 60(4): 2945–2974, 2024] for $p=2$ . PDF    XML

Editorial

2026-03-02

Wolfgang Bock,Kȩstutis Kubilius,Yuliya Mishura,Kostiantyn Ralchenko

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Simulation of supOU processes with specified marginal distribution and correlation function

2026-01-14

Nikolai N. Leonenko,Andrey Pepelyshev

An algorithm is proposed for simulation of superpositions of Ornstein–Uhlenbeck processes which may have short- or long-range dependencies and specified marginal distributions. The algorithm is based on the Bondesson–Rosinski representation of the supOU process as a shot-noise process and enables a clear constructive view on the structure of supOU processes. The use of the proposed algorithm is demonstrated for eight positive marginal distributions and eight entire real line marginal distributions when the explicit formulae for the Lévy density are available or not. PDF    XML