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B1724
Topic: Contributions on dependence models and copulas Title: Closure property of randomly weighted sums with long-tailed increments Authors:  Lina Dindiene - Vilnius University (Lithuania) [presenting]
Remigijus Leipus - Vilnius University (Lithuania)
Abstract: We deal with the tail behavior of randomly weighted sums. We assume that initial random variables $X_1,\dots ,X_n$ are dependent with heavy-tailed distribution functions $F_1, \dots ,F_n$, respectively. Random weights $\Theta_1,\dots , \Theta_n$ are independent of $X_1,\dots ,X_n$. Under some dependence structure between $X_1,\dots ,X_n$ we show that the closure property of the sum $S_n^\Theta \ :=\ \Theta_1 X_1 + \dots +\Theta_n X_n$ holds, i.e., given that distributions $F_1,\dots ,F_n$ are long-tailed, the distribution function of sum $S_n^\Theta$ belongs to the same class. Some copula-based examples illustrate the results.