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Quadratic expansions in optimal investment with respect to perturbations of the semimartingale model

Author

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  • Oleksii Mostovyi

    (University of Connecticut)

  • Mihai Sîrbu

    (The University of Texas at Austin)

Abstract

We study the response of the optimal investment problem to small changes of the stock price dynamics. Starting with a multidimensional semimartingale setting of an incomplete market, we suppose that the perturbation process is also a general semimartingale. We obtain second-order expansions of the value functions, first-order corrections to the optimisers, and provide the adjustments to the optimal control that match the objective function up to the second order. We also give a characterisation in terms of the risk-tolerance wealth process, if it exists, by reducing the problem to the Kunita–Watanabe decomposition under a change of measure and numéraire. Finally, we illustrate the results by examples of base models that allow closed-form solutions, but where this structure is lost under perturbations of the model where our results allow an approximate solution.

Suggested Citation

  • Oleksii Mostovyi & Mihai Sîrbu, 2024. "Quadratic expansions in optimal investment with respect to perturbations of the semimartingale model," Finance and Stochastics, Springer, vol. 28(2), pages 553-613, April.
    • Handle: RePEc:spr:finsto:v:28:y:2024:i:2:d:10.1007_s00780-024-00532-6
    DOI: 10.1007/s00780-024-00532-6
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    References listed on IDEAS

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    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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