标题： 带有交易成本的游戏期权对冲 显示英文标题

标题： Hedging of Game Options With the Presence of Transaction Costs

摘要： 我们研究在比例交易成本下的博弈期权的超复制问题。 我们考虑一个多元连续时间模型，其中贴现股票价格过程满足条件全支撑性质。 我们证明，超复制价格是平凡超复制策略的最低成本。 这个结果是对以前论文（参见[3]和[7]）的扩展，这些论文仅考虑了欧式期权。 在这些论文中，作者表明，在存在比例交易成本的情况下，欧式期权的超复制价格是通过收益函数的凹包来表示的。 在本工作中，我们证明对于博弈期权，超复制价格由标准凹包项的游戏变体给出。 博弈期权的处理更为复杂，需要额外的工具。 我们将一致价格系统理论与在[1]中发展的扩展弱收敛理论相结合。 第二种理论在处理涉及停止时间的对冲时至关重要，例如在博弈期权的情况下。 显示英文摘要

摘要： We study the problem of super-replication for game options under proportional transaction costs. We consider a multidimensional continuous time model, in which the discounted stock price process satisfies the conditional full support property. We show that the super-replication price is the cheapest cost of a trivial super-replication strategy. This result is an extension of previous papers (see [3] and [7]) which considered only European options. In these papers the authors showed that with the presence of proportional transaction costs the super--replication price of a European option is given in terms of the concave envelope of the payoff function. In the present work we prove that for game options the super-replication price is given by a game variant analog of the standard concave envelope term. The treatment of game options is more complicated and requires additional tools. We combine the theory of consistent price systems together with the theory of extended weak convergence which was developed in [1]. The second theory is essential in dealing with hedging which involves stopping times, like in the case of game options.