We analyze the joint extremal behavior of $n$ random products of the form $\prod_{ j=1}^m X_j^{ a_{ ij}}, 1 \leq i \leq n,$ for non-negative, independent regularly varying random variables $X_1, \ldots, X_m$ and general coefficients $a_{ ij} \in \mathbb{ R}$. Products of this form appear for example if one observes a linear time series with gamma type innovations at $n$ points in time. We combine arguments of linear optimization and a generalized concept of regular variation on cones to show that the asymptotic behavior of joint exceedance probabilities of these products is determined by the solution of a linear program related to the matrix $\mathbf{ A}=(a_{ ij})$.
Categories: math.PR