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Research ArticleOpen accessApplication of Markov Chains to Stock TrendsKevin J. Doubleday, Julius N. EsungeProblem statement: Modeling of the Dow Jones Industrial Average is frequently attempted in order to determine trading strategies with maximum payoff. Changes in the DJIA are important since movements may affect both individuals and corporations profoundly. Previous work showed that modeling a market as a random walk was valid and that a market may be viewed as having the Markov … …Journal of Mathematics and Statistics, Vol. 7, Issue 2 · 18 May 2011 · 8,558 accessesView PDFCite
Research ArticleOpen accessDissecting Two Approaches to Energy PricesJulius N. Esunge, Andrew Snyder-BeattieProblem statement: This research tested the viability of Geometric Brownian Motion as a stochastic model of oil prices. Approach: Using autoregressions and unit root tests, we determined that oil prices tend not to exhibit the Markov Property and thus GBM may be a problematic model. Results: Instead, oil prices seem to be mean reverting over the long run, possibly following … …Journal of Mathematics and Statistics, Vol. 7, Issue 2 · 18 May 2011 · 7,100 accessesView PDFCite