Paper: arXiv 2512.01408

Authors: Jose Blanchet, Jiayi Cheng, Hao Liu, Yang Liu

Abstract

We revisit Merton’s continuous-time portfolio selection through a data-driven, distributionally robust lens. Our aim is to tap the benefits of frequent trading over short horizons while acknowledging that drift is hard to pin down, whereas volatility can be screened using realized or implied measures for appropriately selected assets. Rather than time-rectangular distributional robust control – which replenishes adversarial power at every instant and induces over-pessimism – we place a single ambiguity set on the drift prior within a Bayesian Merton model. This prior-level ambiguity preserves learning and tractability: a minimax swap reduces the robust control to optimizing a nonlinear functional of the prior, enabling Karatzas and Zhao \cite{KZ98}-type’s closed-form evaluation for each candidate prior. We then characterize small-radius worst-case priors under Wasserstein uncertainty via an explicit asymptotically optimal pushforward of the nominal prior, and we calibrate the ambiguity radius through a nonlinear Wasserstein projection tailored to the Merton functional. Synthetic and real-data studies demonstrate reduced pessimism relative to DRC and improved performance over myopic DRO-Markowitz under frequent rebalancing.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10 (capped from 7.5: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical contribution by solving the Distributionally Robust Merton Problem using prior-level ambiguity and non-linear Wasserstein projections to reduce over-pessimism. It pairs sophisticated continuous-time stochastic control theory and optimal transport duality with solid synthetic and real-world empirical validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Robust Merton Portfolio Selection<br/>without Over-Pessimism in Continuous Time"] --> B["Data & Inputs:<br/>Asset Prices, Volatility Measures & Nominal Drift Prior"]
    B --> C["Bayesian Ambiguity Set:<br/>Single Wasserstein Ball around Drift Prior"]
    C --> D["Minimax Swap & Portfolio Optimization:<br/>Reduces Control to Nonlinear Prior Functional"]
    D --> E["Nonlinear Wasserstein Projection:<br/>Small-Radius Asymptotics & Radius Calibration"]
    E --> F["Outcomes & Key Findings:<br/>Outperforms DRC & DRO-Markowitz,<br/>Preserves Bayesian Learning, Reduces Pessimism"]

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4 of 137 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.