Year: 2016
East Asian Journal on Applied Mathematics, Vol. 6 (2016), Iss. 2 : pp. 222–234
Abstract
An optimal selection problem for bid and ask quotes subject to a stock inventory constraint is investigated, formulated as a constrained utility maximisation problem over a finite time horizon. The arrivals of buy and sell orders are governed by Poisson processes, and a diffusion approximation is employed on assuming the Poisson arrivals intensity is sufficiently large. Using the dynamic programming principle, we adopt an efficient numerical procedure to solve this constrained utility maximisation problem based on a successive approximation algorithm, and conduct numerical experiments to analyse the impacts of the inventory constraint on a dealer’s terminal profit and stock inventory level. It is found that the stock inventory constraint significantly affects the terminal stock inventory level.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.230515.160316a
East Asian Journal on Applied Mathematics, Vol. 6 (2016), Iss. 2 : pp. 222–234
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: High-frequency trading Limit Order Book (LOB) Diffusion Approximation Hamilton-Jacobi-Bellman (HJB) Equation.