Results 41 to 50 of about 136,850 (323)
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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Large deviations for rough paths of the fractional Brownian motion [PDF]
, 2004 Starting from the construction of a geometric rough path associated with a fractional Brownian motion with Hurst parameter $H\in]{1/4}, {1/2}[$ given by Coutin and Qian (2002), we prove a large deviation principle in the space of geometric rough paths ...
Millet, Annie, Sanz-Solé, Marta
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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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Delay geometric Brownian motion in financial option valuation [PDF]
, 2012 Motivated by influential work on complete stochastic volatility models, such as Hobson and Rogers [11], we introduce a model driven by a delay geometric Brownian motion (DGBM) which is described by the stochastic delay differential equation dSðtÞ ¼ mðSðt
Mao, Xuerong, Sabanis, Sotirios
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On the moments of the integrated geometric Brownian motion
Journal of Computational and Applied Mathematics, 2018 Abstract This note demonstrates how the divided differences characterization for the moments of the integrated geometric Brownian process arises naturally from the solution to their differential equations. The characterization was introduced by Baxter and Brummelhuis in their paper (Baxter and Brummelhuis (2011)) where they demonstrate its ...
Edmond Levy
semanticscholar +2 more sources
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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Option pricing of geometric Asian options in a subdiffusive Brownian motion regime
AIMS Mathematics, 2020 In this paper, pricing problem of the geometric Asian option in a subdiffusive Brownian motion regime is discussed. The subdiffusive property is manifested by the random periods of time, during which the asset price does not change.
Zhidong Guo +2 more
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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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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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Linear drift and entropy for regular covers [PDF]
, 2009 We consider a regular Riemannian cover $\M$ of a compact Riemannian manifold. The linear drift $\ell$ and the Kaimanovich entropy $h$ are geometric invariants defined by asymptotic properties of the Brownian motion on $\M$. We show that $\ell^2 \leq h$
Ledrappier, François
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