We consider the expected utility maximisation problem and its response to small changes in the market price of risk in a continuous semimartingale setting. Assuming that the preferences of a rational economic agent are modelled by a general utility function, we obtain a second-order expansion of the value function, a first-order approximation of the terminal wealth, and we construct trading strategies that match the indirect utility function up to the second order. The method, which is presented in an abstract version, relies on a simultaneous expansion with respect to both the state variable and the parameter, and convex duality in the direction of the state variable only (as there is no convexity with respect to the parameter). If a risk-tolerance wealth process exists, using it as numéraire and under an appropriate change of measure, we reduce the approximation problem to a Kunita–Watanabe decomposition.

中文翻译：

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效用最大化问题对模型摄动的敏感性分析

我们考虑了预期的效用最大化问题及其在连续半市场环境下对风险市场价格微小变化的响应。假设理性经济主体的偏好是由通用效用函数建模的，我们获得了价值函数的二阶展开式，终端财富的一阶近似，并且我们构造了与间接效用函数匹配的交易策略直到第二阶。该方法以抽象形式呈现，它依赖于状态变量和参数的同时展开，以及仅在状态变量方向上的凸对偶性（因为相对于参数没有凸性） 。如果存在风险容忍的财富过程，则将其用作数字，并在适当地改变度量的情况下，