Asymptotics for small nonlinear price impact: A PDE approach to the multidimensional case
Asymptotics for small nonlinear price impact: A PDE approach to the multidimensional case
复制标题
小非线性价格影响的渐近：多维情况的偏微分方程方法
DOI：
10.1111/mafi.12283
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发表时间：
2018
影响因子：
1.6
通讯作者：
Ibrahim Ekren
中科院分区：
文献类型：
--
作者：
Erhan Bayraktar;T. Cayé;Ibrahim Ekren
本文给出了具有小非线性价格影响的多维消费效用最大化问题的价值函数的渐近展开式。在我们的模型中，资产之间的交叉影响是允许的。在小价格影响的极限下，我们确定了价值函数围绕其无摩擦版本的渐近展开式。首阶修正的特征是与遍历控制问题相关的非线性二阶偏微分方程和线性抛物型偏微分方程。我们用一个多元几何布朗运动价格模型来说明我们的结果。
We provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption with small nonlinear price impact. In our model, cross‐impacts between assets are allowed. In the limit for small price impact, we determine the asymptotic expansion of the value function around its frictionless version. The leading order correction is characterized by a nonlinear second‐order PDE related to an ergodic control problem and a linear parabolic PDE. We illustrate our result on a multivariate geometric Brownian motion price model.