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

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  • Oleksii Mostovyi
  • Mihai S^irbu

Abstract

We study the sensitivity of the expected utility maximization problem in a continuous semi-martingale market with respect to small changes in the market price of risk. Assuming that the preferences of a rational economic agent are modeled with a general utility function, we obtain a second-order expansion of the value function, a first-order approximation of the terminal wealth, and construct trading strategies that match the indirect utility function up to the second order. If a risk-tolerance wealth process exists, using it as a num\'eraire and under an appropriate change of measure, we reduce the approximation problem to a Kunita-Watanabe decomposition.

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  • Oleksii Mostovyi & Mihai S^irbu, 2017. "Sensitivity analysis of the utility maximization problem with respect to model perturbations," Papers 1705.08291, arXiv.org.
    • Handle: RePEc:arx:papers:1705.08291
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    References listed on IDEAS

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    Cited by:

    1. Mahan Tahvildari, 2021. "Forward indifference valuation and hedging of basis risk under partial information," Papers 2101.00251, arXiv.org.
    2. Hyungbin Park, 2019. "Convergence rates of large-time sensitivities with the Hansen--Scheinkman decomposition," Papers 1912.03404, arXiv.org, revised Jan 2021.

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