ASYMPTOTIC LINEAR ARBITRAGE AND UTILITY-BASED
ASYMPTOTIC LINEAR ARBITRAGE IN MEAN-REVERTING
FINANCIAL MARKETS
Mbele Bidima Martin Le Doux
University of Yaoundé I, Cameroon
African Institute for Mathematical Sciences
P.O. Box 15780 Yaoundé, CAMEROON
Abstract. Consider a general mean-reverting discrete-time model of financial markets in which the stock prices process is a time discretization of a stochastic differential equation. We introduce a new type of asymptotic arbitrage by proving existence of self-financing strategies that generate linear growing profits on investors' wealth with probability converging to 1 geometrically fast. We estimate the rate of this convergence using ergodic results on Markov chains and large deviations theory.

Next, we discuss asymptotic linear arbitrage in the expected utility sense and its link with the first type of asymptotic arbitrage.

AMS Subject classification: 91G80, 60F10, 60J05
Keywords and phrases: asymptotic linear arbitrage, stochastic control in finance, mean-reverting process, Markov chain, discrete-time Markov processes, large deviations, large deviations principle (LDP)


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DOI: 10.12732/ijam.v27i1.9

Volume: 27
Issue: 1
Year: 2014