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

We study the sensitivity of the expected utility maximization problem ina continuous semi-martingale market with respect to small changes in the market priceof risk. Assuming that the preferences of a rational economic agent... [ view full abstract ]

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