Ruin probabilities under Sarmanov dependence structure

TL;DR

This paper investigates the tail behavior of weighted sums with Sarmanov dependence, extending existing results by relaxing moment conditions, and applies to financial risk models involving regularly varying tails.

Contribution

It provides new sufficient conditions for tail asymptotics of weighted sums under Sarmanov dependence, relaxing previous moment restrictions.

Findings

Derived tail asymptotics for sums with Sarmanov dependence

Relaxed moment conditions on the Y sequence

Applicable to financial risk models with heavy-tailed distributions

Abstract

Our work aims to study the tail behaviour of weighted sums of the form $\sum_{i=1}^{\infty} X_{i} \prod_{j=1}^{i}Y_{j}$, where $(X_{i}, Y_{i})$ are independent and identically distributed, with common joint distribution bivariate Sarmanov. Such quantities naturally arise in financial risk models. Each $X_{i}$ has a regularly varying tail. With sufficient conditions similar to those used by Denisov and Zwart (2007) imposed on these two sequences, and with certain suitably summable bounds similar to those proposed by Hazra and Maulik (2012), we explore the tail distribution of the random variable $\sup_{n \geq 1}\sum_{i=1}^{n} X_i \prod_{j=1}^{i}Y_{j}$. The sufficient conditions used will relax the moment conditions on the $\{Y_{i}\}$ sequence.