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arXiv · 1705.08291

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

Oleksii Mostovyi·Mihai Sîrbu
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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 numéraire and under an appropriate change of measure, we reduce the approximation problem to a Kunita-Watanabe decomposition.

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Oleksii Mostovyi, Mihai Sîrbu. 2017-05-23. Sensitivity analysis of the utility maximization problem with respect to model perturbations. https://arxiv.org/abs/1705.08291

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