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Robust Long-Term Utility Maximization via Risk-Sensitive Control

Article arXiv papers · Author: Thomas Knispel
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Summary

The document studies long-term investment in a stochastic factor model when investors maximize robust expected power utility. Robustness means accounting for an adverse alternative model, rather than optimizing only under a single assumed model. The authors use duality to recast the investment problem as risk-sensitive control over an infinite time horizon.

An ergodic Bellman equation characterizes the optimal long-run growth rate, a corresponding trading strategy, and an asymptotic worst-case model. These results are then used to propose a duality-based approach to a robust large-deviations criterion for long-term investment. The excerpt describes theoretical characterizations rather than a particular asset allocation example or empirical evaluation. It does not state the factor dynamics, market assumptions, solution conditions, or quantitative performance, which limits conclusions about practical implementation.

Key ideas

  • The framework maximizes long-term robust expected power utility in a stochastic factor model.
  • Duality transforms the investment problem into infinite-horizon risk-sensitive control.
  • An ergodic Bellman equation characterizes long-run growth, an optimal strategy, and an asymptotic worst-case model.
  • The results motivate a duality approach to robust large-deviations investment criteria.
  • The excerpt does not specify model assumptions or empirical performance.

Tags

Multi-assetRisk managementPortfolio constructionStatistics
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# Asymptotics of robust utility maximization


# Asymptotics of robust utility maximization









For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $λ\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.

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