Finite-time ruin probability of aggregate Gaussian processes

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

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