Asymptotic Exponential Arbitrage and Utility-Based Asymptotic Arbitrage in Markovian Models of Financial Markets

Acta Applicandae Mathematicae - Tập 138 - Trang 1-15 - 2014
Martin Le Doux Mbele Bidima1, Miklós Rásonyi2,3
1University of Yaoundé I, Yaoundé, Cameroon
2MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary
3University of Edinburgh, Edinburgh, UK

Tóm tắt

Consider a discrete-time infinite horizon financial market model in which the logarithm of the stock price is a time discretization of a stochastic differential equation. Under conditions different from those given in (Mbele Bidima and Rásonyi in Ann. Oper. Res. 200:131–146, 2012), we prove the existence of investment opportunities producing an exponentially growing profit with probability tending to 1 geometrically fast. This is achieved using ergodic results on Markov chains and tools of large deviations theory. Furthermore, we discuss asymptotic arbitrage in the expected utility sense and its relationship to the first part of the paper.

Tài liệu tham khảo