We investigate the asymptotic of ruin probabilities when the company combines the life- and non-life insurance businesses and invests its reserve into a risky asset with stochastic volatility and drift driven by a two-state Markov process. Using the technique of the implicit renewal theory we obtain the rate of convergence to zero of the ruin probabilities.

中文翻译：

---

关于具有随机波动性的股票进行风险投资的破产概率

当公司合并寿险和非寿险业务并将其准备金投资到风险资产时，我们将考察其破产概率的渐近性，该风险资产的波动性和漂移是由两个状态的马尔可夫过程驱动的。使用隐式更新理论的技术，我们得出了破产概率为零的收敛速度。