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arXiv · 2610.13454

Utility-Based Recovery Risk Measures: Redundancy and Approximation for Portfolio Optimization

Justin Plückebaum·Stefan Weber
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Abstract

Recovery risk measures incorporate explicit liability-recovery requirements into asset-liability risk assessment. We study their specialization to optimized certainty equivalents (OCEs), allowing the underlying utility specification to vary across recovery levels and encompassing Recovery Average Value at Risk (RecAV@R) as a special case. For finite recovery specifications, we use the dual penalty representation to characterize redundant recovery regimes and derive position-independent screening conditions. For a subfamily of the Cressie-Read power-divergence family, including entropic and truncated-quadratic specifications, we obtain an exact characterization on atomless probability spaces: universal redundancy is equivalent to a two-dimensional convex-hull condition involving recovery levels and divergence-scale parameters. On such spaces, universal redundancy for RecAV@R reduces to pairwise dominance, whereas for power-divergence OCEs it can arise from the joint effect of several recovery regimes. For nonlinear OCE utilities, we develop a certified piecewise-linear approximation framework for portfolio optimization. In finite-scenario models, the approximating problems are finite-dimensional linear programs, while utility approximation errors transfer directly to the Recovery OCE, yielding explicit error bounds and convergence rates. Uniform approximation over the portfolio domain further implies convergence of optimal values and stability of optimal solutions. A numerical asset-liability study illustrates the effects of recovery-dependent risk preferences and the accuracy and convergence of the approximation.

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Justin Plückebaum, Stefan Weber. 2026-10-09. Utility-Based Recovery Risk Measures: Redundancy and Approximation for Portfolio Optimization. https://arxiv.org/abs/2610.13454

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