高水印费用和漂移不确定性下的终身破产
Lifetime Ruin under High-watermark Fees and Drift Uncertainty
摘要：
本文研究了两个具有高水印费用和漂移不确定性的对冲基金的投资问题，旨在对终身破产问题的研究做出新的贡献。由于每当每个基金利润超过其历史最大值时都会收取多维绩效费，因此价值函数预计是多维的。新的数学挑战出现了标准的降维不能应用，和凸的价值函数和Isaacs条件可能不成立，我们的破产概率最小化问题的漂移不确定性。我们建议采用随机Perron的方法来表征值函数作为唯一的粘性解决方案相关联的Hamilton Jacobi Bellman（HJB）方程，而不诉诸动态规划原理的证明。所需的比较原则，也建立在我们的设置关闭随机Perron的方法的循环。
英文摘要：
This paper aims to make a new contribution to the study of lifetime ruin problem by considering investment in two hedge funds with high-watermark fees and drift uncertainty. Due to multi-dimensional performance fees that are charged whenever each fund profit exceeds its historical maximum, the value function is expected to be multi-dimensional. New mathematical challenges arise as the standard dimension reduction cannot be applied, and the convexity of the value function and Isaacs condition may not hold in our ruin probability minimization problem with drift uncertainty. We propose to employ the stochastic Perron's method to characterize the value function as the unique viscosity solution to the associated Hamilton Jacobi Bellman (HJB) equation without resorting to the proof of dynamic programming principle. The required comparison principle is also established in our setting to close the loop of stochastic Perron's method.
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