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Optimal Consumption Portfolio and No-Arbitrage with Nonproportional Transaction Costs

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Abstract

In this paper we consider a finite-state financial market with non-proportional transaction cost and bid-ask spreads. The transaction cost consists of two parts: a fixed cost and a proportional cost to the size of transaction. We show that the existence of an optimal consumption policy implies that the market has no strong arbitrage; the opposite, however, is not true, i.e., no strong arbitrage does not imply the existence of an optimal consumption policy. This is in sharp contrast with the case of proportional transaction cost and other cases reported in the literature, where no strong arbitrage is equivalent to the existence of an optimal consumption policy. We also study the relationship between weak arbitrage and strong arbitrage. Different from the market with proportional transaction cost, we find that these two forms of arbitrage are equivalent unless the fixed cost is zero. A necessary and sufficient condition for the existence of an optimal consumption policy is also obtained.

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Authors and Affiliations

  1. Department of Industrial Engineering, North Carolina State University, Raleigh, NC, 27695-7906, USA

    X. Chao

  2. Department of Management Sciences, City University of Hong Kong, Kowloon, Hong Kong

    K. K. Lai

  3. Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100080, People’s Republic of China

    Shou-Yang Wang

  4. Institute of Policy and Planning Sciences, University of Tsukuba, Tsukuba, Ibaraki, 305-8573, Japan

    Shou-Yang Wang

  5. School of Business and Finance, University of International Business and Economics, People’s Republic of China

    Mei Yu

Authors
  1. X. Chao
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  2. K. K. Lai
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  3. Shou-Yang Wang
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  4. Mei Yu
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Corresponding author

Correspondence to Shou-Yang Wang.

Additional information

Supported by CAS, NSFC, RGC of Hong Kong and NSF under Grant No. DMI-0196084 and DMI-0200306.

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Chao, X., Lai, K.K., Wang, SY. et al. Optimal Consumption Portfolio and No-Arbitrage with Nonproportional Transaction Costs. Ann Oper Res 135, 211–221 (2005). https://doi.org/10.1007/s10479-005-6242-8

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  • DOI: https://doi.org/10.1007/s10479-005-6242-8

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