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Minimizing Benchmark-Relative Drawdown Duration via Occupation Time Penalization

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  • Jun Sekine
  • Marcus Wunsch

Abstract

We study a continuous-time portfolio optimization problem in which an investor is evaluated relative to a non-replicable benchmark and seeks to control the persistence of benchmark-relative underperformance. We introduce a benchmark-relative drawdown-duration criterion that penalizes the expected discounted time spent in unfavorable benchmark-relative performance states. Despite the path dependence induced by benchmark-relative drawdowns, we show that the problem admits a one-dimensional Markovian representation and derive the associated Hamilton-Jacobi-Bellman equation. We obtain an explicit projection-based characterization of the optimal feedback control, establish a verification theorem, and identify geometric settings under which the associated closed-loop reflected diffusion admits a unique strong solution. Our results provide a tractable downside-risk-oriented alternative to classical benchmark-tracking formulations and reveal a novel projection-based control structure for benchmark-relative risk management.

Suggested Citation

  • Jun Sekine & Marcus Wunsch, 2026. "Minimizing Benchmark-Relative Drawdown Duration via Occupation Time Penalization," Papers 2607.11335, arXiv.org.
    • Handle: RePEc:arx:papers:2607.11335
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    References listed on IDEAS

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