Theory of Probability &Its Applications, Volume 65, Issue 2, Page 249-269, January 2020.
In this paper, we study the ruin problem with investment in a general framework where the business part $X$ is a Lévy process and the return on investment $R$ is a semimartingale. Under some conditions, we obtain upper and lower bounds on the finite and infinite time ruin probabilities as well as the logarithmic asymptotic for them. When $R$ is a Lévy process, we retrieve some well-known results. Finally, we obtain conditions on the exponential functionals of $R$ for ruin with probability 1, and we express these conditions using the semimartingale characteristics of $R$ in the case of Lévy processes.

中文翻译：

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风险资产为半mart时的投资破产问题

概率论及其应用，第65卷，第2期，第249-269页，2020
年1月。在本文中，我们研究了在通用框架中投资的破产问题，其中业务部分$ X $是一个Lévy过程，其收益为投资$ R $是半市场。在某些条件下，我们获得了有限和无限时间破产概率的上限和下限，以及它们的对数渐近线。当$ R $是一个Lévy过程时，我们将检索一些众所周知的结果。最后，我们获得了概率为1的毁灭$ R $指数函数的条件，并且在Lévy过程中，我们使用$ R $的半mart特征来表达这些条件。