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https://scholarbank.nus.edu.sg/handle/10635/162919
Title: | Lifetime Ruin Problem Under High-watermark Fees and Drift Uncertainty | Authors: | Lee, Junbeom Yu, Xiang Zhou, Chao |
Keywords: | q-fin.MF q-fin.MF q-fin.PM Primary, 49L20, 49L25, 60G46, Secondary, 91G10, 93E20 |
Issue Date: | 3-Sep-2019 | Citation: | Lee, Junbeom, Yu, Xiang, Zhou, Chao (2019-09-03). Lifetime Ruin Problem Under High-watermark Fees and Drift Uncertainty. ScholarBank@NUS Repository. | Abstract: | 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. | URI: | https://scholarbank.nus.edu.sg/handle/10635/162919 |
Appears in Collections: | Staff Publications Elements |
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1909.01121v1.pdf | Submitted version | 356.98 kB | Adobe PDF | OPEN | Pre-print | View/Download |
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