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Lifetime Ruin Under High-Water Mark Fees and Drift Uncertainty
Applied Mathematics and Optimization ( IF 1.8 ) Pub Date : 2020-10-30 , DOI: 10.1007/s00245-020-09728-6
Junbeom Lee , Xiang Yu , Chao Zhou

This paper aims to study lifetime ruin minimization 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 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.



中文翻译:

高水位费和漂移不确定性下的终生废墟

本文旨在通过考虑投资两个具有高水印费率和漂移不确定性的对冲基金来研究终生毁灭最小化问题。由于每项基金的利润超过其历史最高值时都会收取多维绩效费,因此价值函数预计将是多维的。由于无法应用标准降维,并且在具有漂移不确定性的概率最小化问题中,值函数的凸性和Isaacs条件可能不成立,因此出现了新的数学挑战。我们建议采用随机Perron方法将值函数表征为相关汉密尔顿-雅各比-贝尔曼的唯一粘度解(HJB)方程而不求助于动态规划原理的证明。在我们的设置中还建立了所需的比较原理,以关闭随机Perron方法的环路。

更新日期:2020-11-02
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