We study the problem of maximising expected utility of terminal wealth under constant and proportional transaction costs in a multidimensional market with prices driven by a factor process. We show that the value function is the unique viscosity solution of the associated quasi-variational inequalities and construct optimal strategies. While the value function turns out to be truly discontinuous, we are able to establish a comparison principle for discontinuous viscosity solutions which is strong enough to argue that the value function is unique, globally upper semicontinuous, and continuous if restricted to either borrowing or non-borrowing portfolios.

中文翻译：

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具有不变和成比例交易成本的因子模型中的效用最大化

我们研究了在多维市场中由要素过程驱动价格的情况下，在不变和成比例的交易成本下最大化终端财富的预期效用的问题。我们证明了价值函数是相关的准变分不等式的唯一粘性解，并构造了最优策略。虽然价值函数确实是真正不连续的，但我们能够为不连续粘度解决方案建立比较原理，该比较原理足以证明价值函数是唯一的，全局上半连续的，并且如果仅限于借用或非借贷，则是连续的借款组合。