Convergence of Markovian price processes in a financial market transaction model

Xiaojing Xu, Jinpeng Ma, Xiaoping Xie

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

This paper studies a financial market transaction model and convergence of Markovian price processes generated by an α-double auction in Xu et al. (Expert Syst Appl 41(16):7032–7045, 2014) and extends their results for a fixed α in [0, 1] to the case where α is governed by a time non-homogeneous Markov chain over a set of finite states defined by R≡ { α1, α2, … , αr} , 0 ≤ α1< α2< ⋯ < αr≤ 1. A convergence result similar to that in Xu et al. (2014) holds, with the fixed α replaced with the average α∗=1r∑θ=1rαθ. We also identify the conditions under which a price process generated by such a Markovian α-double auction converges in probability to a Walrasian equilibrium of the underlying financial market transaction model. A number of simulations are conducted and these simulations are consistent with the theoretical results of the paper.

Original languageEnglish (US)
Pages (from-to)239-273
Number of pages35
JournalOperational Research
Volume17
Issue number1
DOIs
StatePublished - Apr 1 2017

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Strategy and Management
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Computational Theory and Mathematics
  • Management of Technology and Innovation

Keywords

  • Bubble and crash
  • Double auctions
  • Incremental subgradient methods
  • Sentiments
  • Walrasian equilibrium

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