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.
Original language | English |
---|---|
Pages (from-to) | 2743-2773 |
Number of pages | 31 |
Journal | Applied Mathematics and Optimization |
Volume | 84 |
Issue number | 3 |
DOIs | |
Publication status | Published - Dec 2021 |
Keywords
- 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