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摘要翻译：
本文研究了d类资产在具有比例交易费用的离散时间市场模型中未定权益的超级套期保值组合集的显式计算。超级套期保值投资组合的集合可以通过一个包含集合操作的递归构造，在事件树中向后进行。我们将该问题转化为一系列线性向量优化问题，并采用已知的算法进行求解。在树状图中，可以得到相应的超套期保值策略。给出了多个相关资产和篮子期权的例子。此外，我们利用向量优化问题的对偶理论，将现有的标量超套期保值价格计算算法与集值算法联系起来。本文的主要贡献在于建立了与线性向量优化的联系，使得在交易费用下数值求解多资产超额套期保值问题成为可能。
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英文标题：
《An algorithm for calculating the set of superhedging portfolios in
markets with transaction costs》
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作者：
Andreas L\"ohne, Birgit Rudloff
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最新提交年份：
2013
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The set of superhedging portfolios can be obtained by a recursive construction involving set operations, going backward in the event tree. We reformulate the problem as a sequence of linear vector optimization problems and solve it by adapting known algorithms. The corresponding superhedging strategy can be obtained going forward in the tree. Examples are given involving multiple correlated assets and basket options. Furthermore, we relate existing algorithms for the calculation of the scalar superhedging price to the set-valued algorithm by a recent duality theory for vector optimization problems. The main contribution of the paper is to establish the connection to linear vector optimization, which allows to solve numerically multi-asset superhedging problems under transaction costs.
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PDF链接：
https://arxiv.org/pdf/1107.5720
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