Computation of arbitrage in a financial market with various types of frictions

Authors:
Mao-cheng Cai;Xiaotie Deng;Zhongfei Li
Affiliations:
Institute of Systems Science, Chinese Academy of Sciences, Beijing, China;Department of Computer Science, City University of Hong Kong, Hong Kong;Lingnan (University) College, Sun Yat-Sen University, Guangzhou, China
Venue:
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
Year:
2005

Citing 2
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Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
On Computation of Arbitrage for Markets with Friction

COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics

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Abstract

In this paper we study the computational problem of arbitrage in a frictional market with a finite number of bonds and finite and discrete times to maturity. Types of frictions under consideration include fixed and proportional transaction costs, bid-ask spreads, taxes, and upper bounds on the number of units for transaction. We obtain some negative result on computational difficulty in general for arbitrage under those frictions: It is NP-complete to identify whether there exists a cash-and-carry arbitrage transaction and it is NP-hard to find an optimal cash-and-carry arbitrage transaction.