Large deviations and ruin probabilities for solutions to stochastic recurrence equations with heavy-tailed innovations

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Finite-time ruin probability with an exponential Lévy process investment return and heavy-tailed claims (2009, methodology): “Using the theory of stochastic recurrence equations (see Goldie (1991) and Konstantinides and Mikosch (2005)), Klüppelberg and Kostadinova (2008) studied the tail behaviour of the ultimate integrated risk for the discounted net loss process, namely, P{V∞θ > x}, where V∞θ = limt→∞ Vθ(t).”
Integrated insurance risk models with exponential Lévy investment (2008, methodology): “2 in [13], follows that P (Y e−Lθ(E) > x) = P (Y Bθ > x) ∼ E[B θ ]P (Y > x) , x →∞ .”
On a Theorem of Breiman and a Class of Random Difference Equations (2007, background): “Results for regularly varying Q can be found in [13], [17], and [20].”
Tail probabilities for infinite series of regularly varying random vectors (2007, result): “In this particular case, we recover (under identical assumptions) the results of Grey (1994) or Konstantinides and Mikosch (2005), Proposition 2.2.”
Tail asymptotics for exponential function-als of L evy processes (2006, unknown): “Other recent results on this equation leading to Pareto tails can be found in Konstantinides and Mikosch [24] and references therein.”