Papers
WP·2026·002 · April 2026 · Risk · Stochastic Control

Dynamic De-Risking under Drawdown Constraints

Structural Properties and Heuristic Rules for Kelly Betting

By · Market Microstructure Research Lab

Abstract

The classical Kelly criterion maximises long-run growth but does not account for the practical ruin that occurs when a drawdown threshold is breached — a mandate revocation, margin call, or fund liquidation. We study optimal leverage under a hard running-maximum drawdown constraint, modelling the log-distance to the barrier d_t ∈ (0, b] as the state variable. Three main results. First (Theorem 4.1), we show that maximising survival probability degenerates: any interior critical point of the HJB supremand is inadmissible, and the constrained optimum is f* ≡ 0 (hold cash), which is incompatible with the boundary conditions in the class of continuous functions. No smooth, state-dependent de-risking rule emerges from the survival objective. Second (Theorem 4.3), switching to a discounted utility criterion yields a tractable closed-form solution: the power-law value function u(d) = (d/b)^α and the exact optimal leverage f*(d) = κd/(1 − α), where α = 2r/(2r + κ²σ²) ∈ (0, 1). As r → 0, this rule recovers the same normalised linear leverage profile d/b as the Grossman–Zhou proportional-cushion rule, though with a different absolute scale. Third, for practitioners who require an undiscounted, practically calibrated rule, we propose the Exponential DDR f_λ(d) = κ(1 − e^(−λd/b)) as a heuristic approximation to the closed-form control. Monte Carlo validation (N = 50,000 paths, train/test split) shows that the Exponential DDR improves penalised expected log-utility by +15.5% over Grossman–Zhou (56 bps/yr annualised), with identical 100% survival. Robustness tests confirm stable rankings across ruin penalties, rebalancing frequencies (daily and weekly), and transaction costs up to 5 bps. Limitations include the GBM assumption, stylised transaction-cost modelling, and parameter estimation error.

Keywords

  • Kelly criterion
  • Drawdown constraint
  • HJB equation
  • Stochastic control
  • Grossman–Zhou
  • Dynamic de-risking

Cite this paper

Sukhov, S. (2026). Dynamic De-Risking under Drawdown Constraints: Structural Properties and Heuristic Rules for Kelly Betting. MMRL Working Paper WP-2026-002. SSRN. https://doi.org/10.2139/ssrn.6542019

@techreport{sukhov2026dynamic,
  author      = {Sukhov, Sergei},
  title       = {Dynamic De-Risking under Drawdown Constraints: Structural Properties and Heuristic Rules for Kelly Betting},
  institution = {Market Microstructure Research Lab},
  type        = {MMRL Working Paper},
  number      = {WP-2026-002},
  year        = {2026},
  month       = apr,
  doi         = {10.2139/ssrn.6542019},
  url         = {https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6542019},
}

Research area

Drawdown-Constrained Capital Allocation