Results 21 to 30 of about 4,974 (204)
Exact distributions of the maximum and range of random diffusivity processes
New Journal of Physics, 2021 We study the extremal properties of a stochastic process x _t defined by the Langevin equation ${\dot {x}}_{t}=\sqrt{2{D}_{t}}\enspace {\xi }_{t}$ , in which ξ _t is a Gaussian white noise with zero mean and D _t is a stochastic ‘diffusivity’, defined as
Denis S Grebenkov +4 more
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On The Validity of The Geometric Brownian Motion Assumption [PDF]
The Engineering Economist, 2005 Abstract The geometric Brownian motion (GBM) process is frequently invoked as a model for such diverse quantities as stock prices, natural resource prices and the growth in demand for products or services. We discuss a process for checking whether a given time series follows the GBM process.
Marathe, Rahul, Ryan, Sarah
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Discrete Dynamics in Nature and Society, 2021 Since the 2008 financial crisis, it is an important issue to assess the systemic risk of banks, but there is a lack of research on the assessment of the systemic risk of Turkey’s financial system. In addition, geometric Brownian motion is used in most of
Hong Fan, Lingli Feng, Ruoyu Zhou
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Journal of Modern Science, 2022 Objectives The Covid-19 coronavirus pandemic created many doubts and unknowns in all areas of the activity of enterprises, not only for those smaller and more turbulent-prone entities but also for seemingly stronger players on the market. The fundamental
Adam Oleksiuk, Rafał Łochowski
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Cooperation dynamics in networked geometric Brownian motion [PDF]
Physical Review E, 2019 Recent works suggest that pooling and sharing may constitute a fundamental mechanism for the evolution of cooperation in well-mixed fluctuating environments. The rationale is that, by reducing the amplitude of fluctuations, pooling and sharing increases the steady-state growth rate at which the individuals self-reproduce.
Viktor Stojkoski +3 more
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Mirror and synchronous couplings of geometric Brownian motions [PDF]
Stochastic Processes and their Applications, 2014 The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and show that, unlike in the case of ...
Saul D. Jacka +2 more
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Pricing Multidimensional American Options
International Journal of Financial Studies, 2023 A new explicit form is provided for the solution of optimal stopping problems involving a multidimensional geometric Brownian motion. A free-boundary value approach is adopted and the value function is obtained via fundamental solution methods. There are
Elettra Agliardi, Rossella Agliardi
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Applying the IR statistic to estimate the Hurst index of the fractional geometric Brownian motion
Lietuvos Matematikos Rinkinys, 2010 In 2010 J.M. Bardet and D. Surgailis [1] have introduced the increment ratio (IR) statistic which measures the roughness of random paths. It was shown that this statistic was applicable in the cases of diffusion processes driven by the standard Brownian ...
Dimitrij Melichov
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Unraveling trajectories of diffusive particles on networks
Physical Review Research, 2022 The analysis of single-particle trajectories plays an important role in elucidating dynamics within complex environments such as those found in living cells.
Yunhao Sun +5 more
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On the distribution of the time-integral of the geometric Brownian motion
Journal of Computational and Applied Mathematics, 2022 We study the numerical evaluation of several functions appearing in the small time expansion of the distribution of the time-integral of the geometric Brownian motion as well as its joint distribution with the terminal value of the underlying Brownian motion.
Péter Nándori, Dan Pirjol
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