Z. Cui, Y. Wang, “A Breiman's theorem for conditional dependent random vector and its applications to risk theory”, Teor. Veroyatnost. i Primenen., 2025, Volume 70, Issue 2,Pages <nobr>291

This article is cited in 1 paper

A Breiman's theorem for conditional dependent random vector and its applications to risk theory

Z. Cui^a, Y. Wang^b

^a School of mathematics and statistics, Suzhou University of Technology, Suzhou, P. R. China
^b School of Mathematics, Soochow University, Suzhou, P. R. China

Abstract: In this paper, we give a Breiman's theorem for a conditional dependent random vector, where one component has a regularly varying tailed distribution with the index $\alpha\ge0$, while the other component is nonnegative with a more relaxed moment condition. This result substantially extends and improves some existing related results, such as Theorem 2.1 of Yang and Wang [Extremes, 16 (2013), pp. 55–74]. We also provide some concrete examples, some interesting properties, and a construction method of a conditional dependent random vector. Finally, we apply the above Breiman's theorem to risk theory and obtain two asymptotic estimates of the finite-time ruin probability and the infinite-time ruin probability of a discrete-time risk model, in which the corresponding net loss and random discount are conditionally dependent.

Keywords: conditional dependence, Breiman's theorem, regular variation, discrete-time risk model, ruin probabilities, asymptotic estimate.

Received: 09.05.2024
Revised: 19.02.2025
Accepted: 20.02.2025

DOI: 10.4213/tvp5719