We consider the problem of controlling the drift and diffusion rate of the endowment processes of two firms such that the joint survival probability is maximized. We assume that the endowment processes are continuous diffusions, driven by independent Brownian motions, and that the aggregate endowment is a Brownian motion with constant drift and diffusion rate. Our results reveal that the maximal joint survival probability depends only on the aggregate risk-adjusted return and on the maximal risk-adjusted return that can be implemented in each firm. Here the risk-adjusted return is understood as the drift rate divided by the squared diffusion rate.

中文翻译：

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两个合作企业的联合生存概率

我们考虑控制两个企业的禀赋过程的漂移和扩散率以使联合生存概率最大化的问题。我们假设禀赋过程是由独立的布朗运动驱动的连续扩散，并且总禀赋是具有恒定漂移和扩散速率的布朗运动。我们的结果表明，最大联合生存概率仅取决于总风险调整回报以及每个公司可以实现的最大风险调整回报。这里，风险调整回报被理解为漂移率除以扩散率的平方。