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In the insurance business risky investments are dangerous: the case of negative risk sums

机译：在保险业务中，风险投资是危险的：负风险金额的情况

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摘要

We investigate models with negative risk sums when the company invests its reserve into a risky asset whose price follows a geometric Brownian motion. Our main result is an exact asymptotic of the ruin probabilities for the case of exponentially distributed benefits. As in the case of non-life insurance with exponential claims, the ruin probabilities are either decreasing with a rate given by a power function (the case of small volatility) or equal to one identically (the case of large volatility). The result allows us to quantify the share of reserve to invest into such a risky asset to avoid a catastrophic outcome, namely the ruin with probability one. We address also the question of smoothness of the ruin probabilities as a function of the initial reserve for generally distributed jumps.
机译：当公司将其储备金投资到价格遵循几何布朗运动的风险资产时，我们将调查具有负风险总和的模型。我们的主要结果是在指数分布收益的情况下破产概率的精确渐近性。与具有指数索赔的非人寿保险的情况一样，破产概率以幂函数给定的比率降低（波动性较小的情况），或者等于一个等于（波动性较大的情况）。结果使我们能够量化准备投资于这种风险资产的储备份额，以避免灾难性的结果，即可能性为一的破产。我们还讨论了破产概率的平滑度与总体分布跳跃的初始储备的函数关系。

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