Lifetime Ruin Under High-Water Mark Fees and Drift Uncertainty

Junbeom Lee, Xiang Yu, Chao Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2743-2773
Number of pages31
JournalApplied Mathematics and Optimization
Issue number3
Publication statusPublished - Dec 2021


  • Comparison principle
  • Drift uncertainty
  • High-watermark fees
  • Lifetime ruin
  • Multiple hedge funds
  • Stochastic Perron’s method

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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