In this paper, we construct the utility-based optimal hedging strategy for a European-type option in the Almgren-Chriss model with temporary price impact. The main mathematical challenge of this work stems from the degeneracy of the second order terms and the quadratic growth of the first-order terms in the associated Hamilton-Jacobi-Bellman equation, which makes it difficult to establish sufficient regularity of the value function needed to construct the optimal strategy in a feedback form. By combining the analytic and probabilistic tools for describing the value function and the optimal strategy, we establish the feedback representation of the latter. We use this representation to derive an explicit asymptotic expansion of the utility indifference price of the option, which allows us to quantify the price impact in options' market via the price impact coefficient in the underlying market.

中文翻译：

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具有临时价格影响的 Almgren-Chriss 模型中基于效用的定价和或有债权对冲

在本文中，我们为具有临时价格影响的 Almgren-Chriss 模型中的欧式期权构建了基于效用的最优对冲策略。这项工作的主要数学挑战源于相关的 Hamilton-Jacobi-Bellman 方程中二阶项的退化和一阶项的二次增长，这使得建立所需的价值函数的足够规律性变得困难。以反馈形式构建最优策略。通过结合描述价值函数和最优策略的分析和概率工具，我们建立了后者的反馈表示。我们使用这种表示来推导出期权的效用无差异价格的显式渐近扩展，这使我们能够量化期权的价格影响'