Paper: arXiv 2303.01167

Authors: Cosimo Munari, Justin Plückebaum, Stefan Weber

Abstract

We study mean-risk optimal portfolio problems where risk is measured by Recovery Average Value at Risk, a prominent example in the class of recovery risk measures. We establish existence results in the situation where the joint distribution of portfolio assets is known as well as in the situation where it is uncertain and only assumed to belong to a set of mixtures of benchmark distributions (mixture uncertainty) or to a cloud around a benchmark distribution (box uncertainty). The comparison with the classical Average Value at Risk shows that portfolio selection under its recovery version enables financial institutions to exert better control on the recovery on liabilities while still allowing for tractable computations.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides strong mathematical proofs establishing existence results for robust portfolio optimization under Recovery AVaR with distributional uncertainty. However, it is primarily a theoretical contribution with little to no empirical backtesting or real-world data validation shown in the summary.

Research Flowchart

  flowchart TD
    A[Research Goal: Robust Portfolio Selection under Recovery AVaR] --> B[Inputs: Asset Distributions & Uncertainty Sets]
    B --> C1[Mixture Uncertainty]
    B --> C2[Box Uncertainty]
    C1 & C2 --> D[Formulate Mean-Risk Optimization Problem]
    D --> E[Derive Mathematical Existence & Tractability Proofs]
    E --> F[Findings: Better liability recovery control with tractable computation vs. Classical AVaR]