Finite-time ruin probability of aggregate Gaussian processes

TL;DR

This paper derives exact asymptotic formulas for the probability that an aggregate Gaussian risk process exceeds a high threshold within a finite time, considering general trend functions and perturbations.

Contribution

It provides novel asymptotic results for finite-time ruin probabilities of aggregate Gaussian processes with general trends and perturbations, extending existing risk models.

Findings

Exact asymptotics for ruin probabilities as threshold u→∞

Asymptotic results for perturbed Gaussian risk processes

General trend functions considered in the analysis

Abstract

Let $\left\{\sum_{i=1}^n \lambda_i X_i(t), t\in [0,T]\right\}$ be an aggregate Gaussian risk process with $X_i, i\leq n$ independent Gaussian processes satisfying Piterbarg conditions and $\lambda_i$'s given positive weights. In this paper we derive exact asymptotics of the finite-time ruin probability given by $$\mathbb{P}\left(\sup_{t\in[0,T]}\left(\sum_{i=1}^n \lambda_i X_i(t)- g(t) \right)>u\right)$$ as $u\to\infty$ for some general trend function $g$. Further, we derive asymptotic results for the finite-time ruin probabilities of risk processes perturbed by an aggregate Gaussian process.