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Stability of Indirect Utility Under Market Perturbations

Article arXiv papers · Author: Oleksii Mostovyi
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Summary

The document studies how the indirect utility process associated with a trading strategy changes when the risky asset’s return dynamics are perturbed. The strategy need not be optimal, so the analysis also applies to utility processes arising from suboptimal trading decisions.

The authors first establish reverse conjugacy characterizations, then prove continuity and first-order convergence of the indirect utility process when both the finite-variation and martingale components of returns change at the same time. The result describes stability across these two sources of market variation. The brief description does not specify the utility model, assumptions on the perturbations, or quantitative examples, so it offers a theoretical stability result rather than a directly testable trading rule.

Key ideas

  • Indirect utility can be studied for strategies that are not optimal.
  • The analysis considers simultaneous changes in drift-like and martingale return components.
  • Reverse conjugacy characterizations underpin the stability results.
  • The indirect utility process is shown to vary continuously under the stated market perturbations.
  • First-order convergence is established, though the description does not provide detailed assumptions or empirical evidence.

Tags

StatisticsRisk managementPortfolio construction
Full text
# Stability of the indirect utility process


# Stability of the indirect utility process









We investigate the dynamic stability of the indirect utility process associated with a (possibly suboptimal) trading strategy under perturbations of the market. Establishing the reverse conjugacy characterizations first, we prove continuity and first-order convergence of the indirect-utility process under simultaneous perturbations of the finite variation and martingale parts of the return of the risky asset.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.