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http://hdl.handle.net/10397/93888
Title: | Lifetime ruin under high-water mark fees and drift uncertainty | Authors: | Lee, J Yu, X Zhou, C |
Issue Date: | Dec-2021 | Source: | Applied mathematics and optimization, Dec. 2021, v. 84, no. 3, p. 2743-2773 | Abstract: | 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. | Keywords: | Comparison principle Drift uncertainty High-watermark fees Lifetime ruin Multiple hedge funds Stochastic Perron’s method |
Publisher: | Springer | Journal: | Applied mathematics and optimization | ISSN: | 0095-4616 | EISSN: | 1432-0606 | DOI: | 10.1007/s00245-020-09728-6 | Rights: | © Springer Science+Business Media, LLC, part of Springer Nature 2020 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00245-020-09728-6 |
Appears in Collections: | Journal/Magazine Article |
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Yu_Lifetime_Ruin_Under.pdf | Pre-Published version | 1.07 MB | Adobe PDF | View/Open |
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