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On the Geometric Brownian Motion with Alternating Trend
2014A basic model in mathematical finance theory is the celebrated geometric Brownian motion. Moreover, the geometric telegraph process is a simpler model to describe the alternating dynamics of the price of risky assets. In this note we consider a more general stochastic process that combines the characteristics of such two models. Precisely, we deal with
DI CRESCENZO, Antonio +2 more
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Generalizing Geometric Brownian Motion with Bouncing
SSRN Electronic Journal, 2020The trajectories of particles moving in a real line and following the Geometrical Brownian motion have been studied. We take processes and give the generalization of the notions, descriptions and models of Geometrical Brownian motion with bouncing. Moreover, we derive the formulas, which enable us to know the time and positions of the meeting for each ...
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geometric brownian motion with delay
2006A geometric Brownian motion with delay is the solution of a stochastic differential equation where the drift and diffusion coefficient depend linearly on the past of the solution, i.e. a linear stochastic functional differential equation. In this work the asymptotic behavior in mean square of a geometric Brownian motion with delay is completely ...
Riedle, Markus +2 more
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On the moments of the integrated geometric Brownian motion
Journal of Computational and Applied Mathematics, 2018Abstract 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 ...
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Geometric Brownian motion as a model for river flows
Hydrological Processes, 2002AbstractLet X(t) be the flow of a certain river at time t. A geometric Brownian motion process is used as a model for X(t) and is found to give very good forecasts of future flows. The forecasted values generated by this one‐dimensional model are compared with those provided by a deterministic model that requires the evaluation of 18 entries.
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A note on the distribution of integrals of geometric Brownian motion
Statistics & Probability Letters, 2001The purpose of this note is to identify an interesting and surprising duality between the equations governing the probability distribution and expected value functional of the stochastic process defined by At := R t 0 exp{Zs}ds,t 0, where {Zs : s 0} is a one-dimensional Brownian motion with drift coecient µ and diusion coecient 2 .
Enrique Thomann +2 more
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Geometric bounds on certain sublinear functionals of geometric Brownian motion
Journal of Applied Probability, 2003Suppose that {Xs, 0 ≤s≤T} is anm-dimensional geometric Brownian motion with drift,μis a bounded positive Borel measure on [0,T], andϕ: ℝm→ [0,∞) is a (weighted)lq(ℝm)-norm, 1 ≤q≤ ∞. The purpose of this paper is to study the distribution and the moments of the random variableYgiven by theLp(μ)-norm, 1 ≤p≤ ∞, of the functions↦ϕ(Xs), 0 ≤s≤T.
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A New Approach in Geometric Brownian Motion Model
2017Geometric Brownian Motion is One of the basic and useful models applicable in different regions such as Mathematical biology, Financial Mathematics and etc. Its differential is \( dS = \alpha Sdt + \sigma Sdw_{t} \). Where \( \alpha \) and \( \sigma \) are constant and \( w_{t} \) is Wiener process.
Abdolsadeh Neisy +1 more
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Exit probability for an integrated geometric Brownian motion
Statistics & Probability Letters, 2009In this note, we present an explicit form for the exit probability of an integrated geometric Brownian motion from a given curved domain. Explicit bounds for the exit probability and one possible application are also given, under certain conditions.
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A Short Note on Absorbed Geometric Brownian Motions
SSRN Electronic Journal, 2016Our aim is to give an explicit expression of the cumulative density function of an absorbed stochastic process at terminal time T. This process is the wealth process induced by holding a stock following a geometric Brownian motion and investing this amount in the money market account as soon as the stock hits a lower, time-dependent threshold.
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