# Heavy Tails for an Alternative Stochastic Perpetuity Model

## TL;DR

This paper introduces a stochastic perpetuity model with independent discount factors, demonstrating that its distribution tails are regularly varying with a logarithmic correction, differing from classical models.

## Contribution

It presents a novel perpetuity model with independent discount factors and characterizes its tail behavior, revealing a logarithmic term in the tail asymptotics.

## Key findings

- Tails are regularly varying in univariate and multivariate cases.
- Distribution tails involve a logarithmic correction, unlike pure power laws.
- The model extends classical perpetuity models by incorporating additional randomness.

## Abstract

In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten [12] and Goldie [8] all discount factors in the model are mutually independent. We prove that the tails of the distribution of this model are regularly varying both in the univariate and multivariate cases. Due to the additional randomness in the model the tails are not pure power laws as in the Kesten-Goldie setting but involve a logarithmic term.