A risk‐averse agent hedges her exposure to a nontradable risk factor U using a correlated traded asset S and accounts for the impact of her trades on both factors. The effect of the agent's trades on U is referred to as cross‐impact. By solving the agent's stochastic control problem, we obtain a closed‐form expression for the optimal strategy when the agent holds a linear position in U. When the exposure to the nontradable risk factor is nonlinear, we provide an approximation to the optimal strategy in closed‐form, and prove that the value function is correctly approximated by this strategy when cross‐impact and risk‐aversion are small. We further prove that when is nonlinear, the approximate optimal strategy can be written in terms of the optimal strategy for a linear exposure with the size of the position changing dynamically according to the exposure's “Delta” under a particular probability measure.

中文翻译：

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通过交易成本和价格影响对冲不可交易的风险

规避风险的经纪人使用相关的交易资产S对冲至不可交易的风险因子U的套期保值，并说明其交易对这两个因素的影响。代理交易对U的影响称为交叉影响。通过解决代理的随机控制问题，当代理在U中保持线性位置时，我们可以获得最优策略的闭式表达式。当不可交易风险因素的风险为非线性时，我们以封闭形式提供最佳策略的近似值，并证明当交叉影响和风险规避较小时，该策略可以正确地逼近价值函数。我们进一步证明 如果是非线性的，则可以根据线性曝光的最佳策略来编写近似最佳策略，在特定的概率度量下，位置的大小会根据曝光的“ Delta”动态变化。