Excess profit relative to the benchmark asset under the $ \alpha $-confidence level

Dong Ma; Peibiao Zhao; Minghan Lyu; Jun Zhao; Dong Ma; Peibiao Zhao; Minghan Lyu; Jun Zhao

doi:10.3934/math.20231553

AIMS Mathematics

2023, Volume 8, Issue 12: 30419-30428. doi: 10.3934/math.20231553

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Research article

Excess profit relative to the benchmark asset under the $ \alpha $-confidence level

1.
School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing, Jiangsu, China
2.
Shanghai National Accounting Institute, Shanghai, China
3.
School of Science, Xi'an University of Posts and Telecommunications, Xi'an, Shaanxi, China

Received: 28 July 2023 Revised: 22 October 2023 Accepted: 01 November 2023 Published: 09 November 2023
MSC : 91G30, 91G80

We introduce a generalized concept of arbitrage, excess profit relative to the benchmark asset under $ \alpha $-confidence level, $ \alpha $-REP, in a single-period market model with proportional transaction costs. We obtain a fundamental theorem of asset pricing with respect to the absence of $ \alpha $-REP. Moreover, we discuss the relationships between classical arbitrage, strong statistical arbitrage and $ \alpha $-REP.
- arbitrage,
- excess profit,
- confidence level,
- fundamental theorem of asset pricing
Citation: Dong Ma, Peibiao Zhao, Minghan Lyu, Jun Zhao. Excess profit relative to the benchmark asset under the $ \alpha $-confidence level[J]. AIMS Mathematics, 2023, 8(12): 30419-30428. doi: 10.3934/math.20231553

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Abstract

We introduce a generalized concept of arbitrage, excess profit relative to the benchmark asset under $ \alpha $-confidence level, $ \alpha $-REP, in a single-period market model with proportional transaction costs. We obtain a fundamental theorem of asset pricing with respect to the absence of $ \alpha $-REP. Moreover, we discuss the relationships between classical arbitrage, strong statistical arbitrage and $ \alpha $-REP.

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