Convergence of Markovian price processes in a financial market transaction model

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, … , α_r} , 0 ≤ α₁< α₂< ⋯ < α_r≤ 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.