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Generalised Geometric Brownian Motion: Theory and Applications to Option Pricing [PDF]
Entropy, 2020 Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for asset dynamics, due to ...
Viktor Stojkoski +4 more
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Entropy corrected geometric Brownian motion [PDF]
Scientific ReportsThe geometric Brownian motion (GBM) is widely used for modeling stochastic processes, particularly in finance. However, its solutions are constrained by the assumption that the underlying distribution of returns follows a log-normal distribution.
Rishabh Gupta +3 more
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Ergodicity breaking in wealth dynamics: The case of reallocating geometric Brownian motion [PDF]
Physical Review E, 2022 A growing body of empirical evidence suggests that the dynamics of wealth within a population tends to be nonergodic, even after rescaling the individual wealth with the population average.
Viktor Stojkoski, Marko Karbevski
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Mathematics, 2021 In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best ...
Vasile Brătian +4 more
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Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity [PDF]
Philosophical Transactions of the Royal Society A, 2021 We explore the role of non-ergodicity in the relationship between income inequality, the extent of concentration in the income distribution, and income mobility, the feasibility of an individual to change their position in the income rankings.
Viktor Stojkoski +5 more
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Geometric Brownian motion under stochastic resetting: A stationary yet nonergodic process [PDF]
Physical Review E, 2021 We study the effects of stochastic resetting on geometric Brownian motion with drift (GBM), a canonical stochastic multiplicative process for nonstationary and nonergodic dynamics.
Viktor Stojkoski +3 more
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Arbitrage Problems with Reflected Geometric Brownian Motion [PDF]
Finance and Stochastics, 2022 Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free.
Dean Buckner, Kevin Dowd, Hardy Hulley
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Frontiers in Applied Mathematics and StatisticsThis research is devoted to studying a geometric Brownian motion with drift switching driven by a 2 × 2 Markov chain. A discrete-time multiplicative approximation scheme was developed, and its convergence in Skorokhod topology to the continuous-time ...
Vitaliy Golomoziy +2 more
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Geometric Brownian motion and a new approach to the spread of Covid-19 in Italy
Gulf Journal of Mathematics, 2021 Starting from the problem of the asymmetry of the curve, a new model is adoptedfor the spread of Covid-19. The pandemic waves are modelled from a geometric Brownian motion, leading to a lognormal distribution.
Nicola Fabiano, Stojan Radenović
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Physical Review ResearchThe translational motion of anisotropic or self-propelled colloidal particles is closely linked with the particle’s orientation and its rotational Brownian motion.
Felix Höfling, Arthur V. Straube
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