Path-Space Robust Bayesian Portfolio Selection

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Highly relevant to quantitative trading theory. Provides closed-form robust portfolio policies under model misspecification with Bayesian learning. The cubic correction (Theorem 7.1) directly informs position sizing: investors should reduce large positions when the posterior signal is strong but potentially wrong. The price-of-robustness formula (V1 = ½ Var[(X*_T - w)²]) quantifies the insurance cost. The dichotomy between constant-multiplier and value-scaled robustness clarifies when robustness changes policy shape vs. merely rescaling. However, the single-asset, known-volatility setting limits direct practical deployment without extension.

The closed-form results (Riccati systems, kurtosis identity, cubic correction) are analytically tractable and implementable. The Cole-Hopf reduction, pathwise identity (Lemma 5.1), and Riccati trap (Theorem 6.3) provide explicit formulas. However, the conditional verification (Assumption 8.2), the open two-sided remainder, and the need for truncated feedbacks in practice add complexity. The finite-difference solver for benchmarking (Figure 3b) requires careful upwind scheme implementation. Multi-asset extension would significantly increase complexity.

Purely theoretical paper with all results in closed form. No empirical data or code required. Key formulas (Theorems 5.2, 6.3, 7.1, 7.3) are fully explicit. Numerical illustrations (Figures 1-3) use closed-form expressions and a finite-difference solver described in the text. Reproducibility is high for the analytical results; the open verification problem (Assumption 8.2) and two-sided remainder bound are acknowledged as unresolved.