We consider two insurance companies with endowment processes given by Brownian motions with drift. The firms can collaborate by transfer payments in order to maximize the probability that none of them goes bankrupt. We show that pushing maximally the company with less endowment is the optimal strategy for the collaboration if the Brownian motions are correlated and the transfer rate can exceed the drift rates. Moreover, we obtain an explicit formula for the minimal ruin probability in case of perfectly positively correlated Brownian motions where we also allow for different diffusion coefficients.

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具有相关布朗运动的二维模型中的毁坏概率

我们考虑两个保险公司，其禀赋过程由带漂移的布朗运动给出。公司可以通过转移支付进行合作，以最大限度地提高它们都不破产的可能性。我们表明，如果布朗运动相关并且转移率可以超过漂移率，则最大限度地推动禀赋较少的公司是合作的最佳策略。此外，在完全正相关布朗运动的情况下，我们获得了最小毁坏概率的明确公式，其中我们还允许不同的扩散系数。