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

*Oleksii Mostovyi* and
*Mihai S\^irbu*

Papers from arXiv.org

**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.

**New Economics Papers:** this item is included in nep-upt

**Date:** 2017-05

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**Persistent link:** https://EconPapers.repec.org/RePEc:arx:papers:1705.08291

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