ABSTRACT
This paper presents a framework for analyzing the asymptotic tail behavior of multivariate randomly weighted sums with dependent weights, extending classical concepts and providing conditions for tail asymptotics without moment conditions on weights.
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Key findings
Novel definition of multivariate quasi-asymptotic independence for randomly weighted sums.
Extension of Breiman’s theorem to dependent multivariate weights under relaxed moment conditions.
Second-order asymptotic expansions for joint tail probabilities.
Uniform asymptotic results for finite-time ruin probabilities in multidimensional risk models.
Limitations & open questions
Further research needed for more complex dependence structures and applications in other fields.