Sensitivity analysis of the utility maximisation problem with respect to model perturbations
Sensitivity analysis of the utility maximisation problem with respect to model perturbations
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DOI：
10.1007/s00780-019-00388-1
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发表时间：
2019-07-01
影响因子：
1.7
通讯作者：
Sirbu, Mihai
中科院分区：
文献类型：
--
作者：
Mostovyi, Oleksii;Sirbu, Mihai
我们考虑了期望效用最大化问题及其对连续半鞅环境下市场风险价格微小变化的响应。假设理性经济主体的偏好由一般效用函数建模，我们得到了价值函数的二阶展开式、终端财富的一阶近似，并构建了匹配间接效用函数至二阶的交易策略。该方法以抽象形式呈现，依赖于对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）。如果存在风险容忍财富过程，将其作为数值，并在适当的测度变化下，将近似问题简化为Kunita-Watanabe分解。
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, afirst-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). Ifa risk-tolerance wealth process exists, using it as numeraire and under an appropriate change of measure, we reduce the approximation problem to a Kunita-Watanabe decomposition.