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Sensitivity analysis of the utility maximisation problem with respect to model perturbations

Author

Listed:
  • Oleksii Mostovyi

    (University of Connecticut)

  • Mihai Sîrbu

    (The University of Texas at Austin)

Abstract

We consider the expected utility maximisation problem and its response to small changes in the market price of risk in a continuous semimartingale setting. Assuming that the preferences of a rational economic agent are modelled by a general utility function, we obtain a second-order expansion of the value function, a first-order approximation of the terminal wealth, and we construct trading strategies that match the indirect utility function up to the second order. The method, which is presented in an abstract version, relies on a simultaneous expansion with respect to both the state variable and the parameter, and convex duality in the direction of the state variable only (as there is no convexity with respect to the parameter). If a risk-tolerance wealth process exists, using it as numéraire and under an appropriate change of measure, we reduce the approximation problem to a Kunita–Watanabe decomposition.

Suggested Citation

  • Oleksii Mostovyi & Mihai Sîrbu, 2019. "Sensitivity analysis of the utility maximisation problem with respect to model perturbations," Finance and Stochastics, Springer, vol. 23(3), pages 595-640, July.
    • Handle: RePEc:spr:finsto:v:23:y:2019:i:3:d:10.1007_s00780-019-00388-1
    DOI: 10.1007/s00780-019-00388-1
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. David M. Kreps & Walter Schachermayer, 2020. "Convergence of optimal expected utility for a sequence of discrete‐time markets," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1205-1228, October.
    2. Sarah Boese & Tracy Cui & Samuel Johnston & Gianmarco Molino & Oleksii Mostovyi, 2020. "Stability and asymptotic analysis of the F\"ollmer-Schweizer decomposition on a finite probability space," Papers 2002.03286, arXiv.org, revised Jun 2020.
    3. Friedrich Hubalek & Walter Schachermayer, 2021. "Convergence of optimal expected utility for a sequence of binomial models," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1315-1331, October.
    4. Hyungbin Park & Heejun Yeo, 2022. "Dynamic and static fund separations and their stability for long-term optimal investments," Papers 2212.00391, arXiv.org, revised Mar 2023.
    5. Mostovyi, Oleksii, 2020. "Asymptotic analysis of the expected utility maximization problem with respect to perturbations of the numéraire," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4444-4469.
    6. Daniel Bartl & Ariel Neufeld & Kyunghyun Park, 2023. "Sensitivity of robust optimization problems under drift and volatility uncertainty," Papers 2311.11248, arXiv.org.

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    More about this item

    Keywords

    Sensitivity analysis; Optimal investment; Duality theory; Kunita–Watanabe decomposition;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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