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Research

Portfolio optimization at the seam of operations research and machine learning — what I work on, and what I've published.

Research interests

  • Multi-period portfolio optimization Allocation across horizons, rebalancing as conditions change — not single-shot mean–variance.
  • Risk parity & hierarchical methods Distributing risk across structure — sectors, then assets — rather than chasing returns.
  • Reinforcement learning for allocation Policies that learn to allocate under uncertainty, instead of assuming a fixed model.
  • Operations research & convex optimization The constraints, duality, and structure underneath it all — the OR core of the PhD.

Selected research

q-fin.PM · Portfolio Management

Optimal Portfolio Construction — A Reinforcement-Learning-Embedded Bayesian Hierarchical Risk Parity (RL-BHRP) Approach

S. Kang, Z. Tian · arXiv preprint · arXiv:2508.11856 · 2025

The idea

Most portfolios either assume a fixed model of risk or chase returns directly. RL-BHRP does neither: it spreads risk hierarchically across sectors and the stocks within them, then uses reinforcement learning to adapt those exposures as market conditions shift — learning how to allocate, rather than assuming.

Allocation that learns instead of assuming — diversified and investable, not a backtest curiosity.

The method, formally

wi=Wg(i) ηi∣g(i)w_i = W_{g(i)}\,\eta_{i\mid g(i)}
Two-level weights — each holding is its sector’s share times its share within that sector.
Ut+1=wt⊤Rt+1−c∥wt−wt−1∥1−λ[αVwithin+(1−α)Vacross]\begin{aligned} U_{t+1} = {}& w_t^{\top} R_{t+1} - c\lVert w_t - w_{t-1}\rVert_1 \\ &{} - \lambda\big[\alpha V_{\text{within}} + (1-\alpha) V_{\text{across}}\big] \end{aligned}
The learning signal: gross return, minus turnover cost, minus a risk-dispersion penalty.
∑i=1NRCi(w)=σp2(w)\sum_{i=1}^{N} \mathrm{RC}_i(w) = \sigma_p^2(w)
Risk contributions sum exactly to portfolio variance — the basis for parity.
Σ~gh=(η(g))⊤Σgh η(h)\tilde{\Sigma}_{gh} = (\eta^{(g)})^{\top}\Sigma_{gh}\,\eta^{(h)}
Within-sector weights aggregate asset covariance up to the sector level.

Equations from arXiv:2508.11856.

Results · out-of-sample

~120%
wealth compounded, out-of-sample 2020–25 (vs 101% static, 91% sector ETF)
~15% / yr
average annual growth (vs 13% and 12%)
comparable
drawdowns — value added while staying diversified
Metric RL-BHRPBHRPBenchmark
Cumulative return 1.201.010.91
CAGR 15.2%13.4%12.3%
Annual volatility 17.4%16.5%17.3%
Sharpe 0.900.850.76
Sortino 1.651.531.37
Max drawdown −20.3%−19.1%−18.3%
Calmar 0.750.700.67
Information ratio 0.690.22—
CVaR 5% −10.2%−9.7%−10.3%
Hit rate (>0) 64.2%64.2%62.7%
Full period · 2020-02 to 2025-08 · RL-BHRP vs static BHRP vs sector benchmark
Read the paper · arXiv ↗ PDF ↗

Earlier work

D. Li, Z. Tian, Y. Duan2022

Self-Attention on RNN-based Text Classification

CNSSE / SPIE, vol. 12290