This paper investigates the asymptotic behavior of randomly weighted sums in continuous-time risk models driven by Lévy processes. It establishes tail asymptotics for aggregate claims processes with randomly discounted losses, where claim sizes follow heavy-tailed distributions and discount factors are modeled as general stochastic processes. The framework extends classical results on subexponential asymptotics to dependent increments and random weights without restrictive moment conditions.
Key findings
Establishes tail asymptotics for randomly weighted sums under upper tail asymptotic independence conditions.
Develops uniform asymptotic results for stopped sums and continuous-time processes.
Obtains explicit asymptotics for regularly varying tails via an extension of Breiman’s theorem.
Applies results to derive asymptotic formulas for ruin probabilities in Lévy risk models with random discounting.
Limitations & open questions
Further research needed for practical implementation in real-world insurance risk management.