EQUIVALENCE OF PARTICLE SURVIVAL MODEL AND RECORD VALUE PROCESS, AND ITS NEW APPLICATION TO LIMIT ORDER BOOKS

Abstract

The particle survival model, which was originally proposed to analyze the dynamics of species’ coexistence, has surprisingly found to be related to a non-homogeneous Poisson process. It is also well known that successive record values of independent and identically distributed sequences have the spatial distribution of such processes. In this paper, we show that the particle survival model and the record value process are indeed equivalent. Further, we study their application to determine the optimal strategy for placing selling orders on stock exchange limit order books. Our approach considers the limit orders as particles, and assumes that the other traders have zero intelligence.