5 articles for “Ornstein-Uhlenbeck (OU)”

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Research ArticleOpen accessEvery word in the titleModification of the Ornstein Uhlenbeck Process to Incorporate the Influence of Speculation on Volatility in Financial MarketsHendrietha Joan Hendricks, Jacob Ongala, Dismas NtirampebaFinancial market participants often speculate on how markets would behave in the light of certain information at hand. This speculation contributes to volatility within the financial market and consequently, it makes the market unstable. The Ornstein Uhlenbeck (OU) model has intensively been used in modelling volatility, however, the contribution of speculation on volatility has not been studied in the OU … …Journal of Mathematics and Statistics, Vol. 18, Issue 1 · 18 Jan 2022 · 7,172 accessesView PDF Cite

Research ArticleOpen accessEvery word in the titleComparing the Empirical and the Theoretical Probability Density of Return in which Variance Obeying Ornstein-Uhlenbeck Process at Indonesian Stock Exchange IDXDwi Satya Palupi, Eduardus Tandelilin, Arief Hermanto, Muhammad Farchani RosyidThe distribution of the probability density of a return index with stochastic volatility has been calculated. Here the stock index is assumed to follow geometric Brownian motion, while the variance is assumed to obey Ornstein-Uhlenbeck process as in Heston model. The distribution of the probability density of the return which is obtained by solving the Fokker-Planck equation of two dimensional … …American Journal of Applied Sciences, Vol. 14, Issue 9 · 17 May 2017 · 7,625 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsDissecting 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 PDF Cite

Research ArticleOpen accessIn the abstractIntegrating Stochastic Properties into Traffic Flow Modeling: A Stimulus-Response ApproachKonate N’Golo, Mark Kimathi, Emile DanhoHighway traffic congestion, characterized by its inherent instability, has been extensively studied using deterministic models, providing valuable insights. However, these models often overlook the stochastic nature of driver behavior, a key factor that significantly impacts traffic flow. Recognizing this, a car-following model with discretionary lane changes to analyze their effect on traffic dynamics was introduced. While the mathematical results were … …Journal of Mathematics and Statistics, Vol. 20, Issue 1 · 19 Dec 2024 · 7,153 accessesView PDF Cite

Research ArticleOpen accessIn the abstractIntroduction to the Besov Spaces and Triebel-Lizorkin Spaces for Hermite and Laguerre expansions and some applicationsA. Iris, P. LopezWe introduced new definitions of Besov spaces and Triebel-Lizorkin spaces associated with multidimensional Hermite expansions and multidimensional Laguerre expansions. We showed that the set of p-integrable functions is a Triebel-Lizorkin space with respect to the Gaussian measure and similarly, with respect to the probabilistic Gamma measure. Also, we showed that the Gaussian Sobolev spaces and Laguerre Sobolev spaces are Triebel-Lizorkin … …Journal of Mathematics and Statistics, Vol. 1, Issue 3 · 30 Sep 2005 · 7,580 accessesView PDF Cite