Asymptotics of ruin probabilities for controlled risk processes in the small claims case

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Ruin Models with Investment Income (2008, unknown): “led case, i.e. when MS(κ) = E[eκS] <∞ for some κ>0, the results do not diﬀer very much from those in the diﬀusion case. Although A∗ t is not a constant, when rf = 0 and B = {1}, it is proved in [21, 31] that limy→∞ A ∗(y) = A0 >0 and also that lim y→∞ eκ∗yψa∗(y) = γ>0 where κ∗ is the pos”
Some Applications and Methods of Large Deviations in Finance and Insurance (2007, background): “processes (e.g. Levy proceses) for the risk reserve, heavy-tailed distribution for the claim size ... In the next paragraph, we study an extension of the classical ruin problem, developed by [23] and [31], wherethe insurerhas the additional opportunityto invest in a stock market. Application : Impor”
Asymptotic ruin probabilities and optimal investment (2003, background): “Remark. It has been shown recently (after the submission of this paper) by Hipp and Schmidli [ 12 ] that the function k⁄(x) possesses a limit, for x!1.”