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首页> 外文期刊>Journal of Applied Probability >Asymptotic ruin probabilities for a bivariate lévy-driven risk model with heavy-tailed claims and risky investments
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Asymptotic ruin probabilities for a bivariate lévy-driven risk model with heavy-tailed claims and risky investments

机译：具有重尾索赔和风险投资的双变量lévy驱动风险模型的渐近破产概率

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摘要

Consider a general bivariate Lévy-driven risk model. The surplus process Y, starting with Y_0 = x > 0, evolves according to dY _t = Y_t - dR_t - dP_t for t > 0, where P and R are two independent Lévy processes respectively representing a loss process in a world without economic factors and a process describing the return on investments in real terms. Motivated by a conjecture of Paulsen, we study the finite-time and infinitetime ruin probabilities for the case in which the loss process P has a Lévy measure of extended regular variation and the stochastic exponential ofR fulfills a moment condition. We obtain a simple and unified asymptotic formula as x → ∞, which confirms Paulsen's conjecture.
机译：考虑一个一般的双变量Lévy驱动的风险模型。对于t> 0，从Y_0 = x> 0开始的剩余过程Y根据dY _t = Y_t-dR_t-dP_t演化，其中P和R是两个独立的Lévy过程，分别表示在没有经济因素和实际描述投资回报的过程。受保尔森猜想的启发，我们研究了损失过程P具有扩展的规律变化的Lévy测度并且R的随机指数满足矩条件的情况的有限时间和无限时间破产概率。我们获得了x→∞的简单统一的渐近公式，这证实了保尔森的猜想。

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