{"ID":6537603,"CreatedAt":"2026-07-14T02:54:43.516908796Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.11335","arxiv_id":"2607.11335","title":"Minimizing Benchmark-Relative Drawdown Duration via Occupation Time Penalization","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.","short_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...","url_abs":"https://arxiv.org/abs/2607.11335","url_pdf":"https://arxiv.org/pdf/2607.11335v1","authors":"[\"Jun Sekine\",\"Marcus Wunsch\"]","published":"2026-07-13T09:53:18Z","proceeding":"q-fin.MF","tasks":"[\"q-fin.MF\",\"math.OC\"]","methods":"[\"Diffusion Model\",\"Large Language Model\"]","has_code":false}