套利
数学优化
计算
计算机科学
上下界
衍生工具(金融)
对偶(序理论)
效用最大化问题
数理经济学
效用最大化
数学
经济
财务
算法
离散数学
数学分析
作者
Ariel Neufeld,Antonis Papapantoleon,Qikun Xiang
出处
期刊:Management Science
[Institute for Operations Research and the Management Sciences]
日期:2023-04-01
卷期号:69 (4): 2051-2068
被引量:4
标识
DOI:10.1287/mnsc.2022.4456
摘要
We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices. We work in a completely realistic setting, in that we only assume the knowledge of traded prices for other single- and multi-asset derivatives and even allow for the presence of bid–ask spread in these prices. We provide a fundamental theorem of asset pricing for this market model, as well as a superhedging duality result, that allows to transform the abstract maximization problem over probability measures into a more tractable minimization problem over vectors, subject to certain constraints. Then, we recast this problem into a linear semi-infinite optimization problem and provide two algorithms for its solution. These algorithms provide upper and lower bounds for the prices that are ε-optimal, as well as a characterization of the optimal pricing measures. These algorithms are efficient and allow the computation of bounds in high-dimensional scenarios (e.g., when d = 60). Moreover, these algorithms can be used to detect arbitrage opportunities and identify the corresponding arbitrage strategies. Numerical experiments using both synthetic and real market data showcase the efficiency of these algorithms, and they also allow understanding of the reduction of model risk by including additional information in the form of known derivative prices. This paper was accepted by Chung Piaw Teo, optimization. Funding: This work was supported by the Nanyang Technological University [NAP Grant] and the Hellenic Foundation for Research and Innovation [Grant HFRI-FM17-2152]. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2022.4456 .
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