Constrained stochastic estimation algorithms for a class of hybrid stock market models
type: Item
instance of: scholarly article
title: Constrained stochastic estimation algorithms for a class of hybrid stock market models
zbMATH Open document ID: 1050.91053
DOI: 10.1023/A:1024795626350
author: K. Yin
author: G. Yin
author: Q. Zhang
published in: Journal of Optimization Theory and Applications
publication date: 2003-09-15T00:00:00Z
review text: The authors consider the stock market as a hybrid system, in which continuous dynamics and discrete events coexist. The motivation stems from the need for suitable models to better capture the price movement on an individual stock. They model random behavior of equity markets with the help of integrating a hidden, continuous-time Markov chain with a finite state space into the original system equation. This chain has influence on both the return rate and the volatility. A stochastic optimization algorithm for the estimation of the generator of the chain is designed, its convergence is proved, the rate of convergence is derived and its performance using both simulation and real data is examined. The hybrid model is compared to the usual model based on geometric Brownian motion and it is demonstrated that the hybrid geometric Brownian motion model is better in terms of the corresponding least squares error. Also it is shown how to use the estimated generator in making stock liquidation decisions.
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 90C15
zbMATH DE Number: 1981577
zbMATH Keywords: stochastic optimization
zbMATH Keywords: Markov chains
zbMATH Keywords: geometric Brownian motion
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
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full work available at URL: a:1024795626350
OpenAlex ID: W21271374
description: scientific article; zbMATH DE number 1981577