On Asymptotic Linear Arbitrage in Markovian Models of Financial Markets

Abstract

Consider an investor's wealth allocated in a stock with prices modeled as a discretetime homogeneous Markov process that is not necessarily specied by any stochastic recursion unlike in our previous paper (Mbele Bidima (2014)). Under this modied modeling setting and more stringent (but still veriable) conditions, using dierent tools of Branching processes and Large deviations of functions of Markov transitions, we show again existence of asymptotic linear arbitrage with geometrically decaying failure probability in such a market model.

Keyword: Asymptotic linear arbitrage, Markov process, Large deviations