Corpus ID: 126350882

Optimal Transport on the Probability Simplex with Logarithmic Cost

  title={Optimal Transport on the Probability Simplex with Logarithmic Cost},
  author={Gabriel Khan and Jun Zhang},
  journal={arXiv: Optimization and Control},
  • Gabriel Khan, J. Zhang
  • Published 30 November 2018
  • Mathematics, Economics
  • arXiv: Optimization and Control
Motivated by the financial problem of building financial portfolios which outperform the market, Pal and Wong considered optimal transport on the probability simplex $\triangle^n$ where the cost function is induced by the free energy. We study the regularity of this problem and find that the associated $MTW$ tensor is non-negative definite and in fact constant on $\triangle^n \times \triangle^n$. We further find that relative $c$-convexity corresponds to the standard notion of convexity in the… Expand
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